My friend and I took off for a section of the Sierra High Route last week and got back in the wee hours yesterday. The spring conditions gave us snow, granite, some dirt, and ice. We spent some time on the JMT/PCT as well which I’ve come to nickname “the highway” : full of people, busy, and usually littered.
It used to be rare to see a PCT thru-hiker, now mid season you’ll easily encounter 20 per day in addition to other trail users. Not a Disneyland mob by any means, but enough to break you from the isolation of the Eastern Sierras.

Forget daily mileage, think daily hours and your schedule.
A reality for cross country travel especially on mixed terrain is that you will go slow. Specifically how slow is a crap shoot, but slow it will be. Maybe 1/3 – 1/4 of your trail speed.
Far more important (trails or cross country / mountaineering) is your daily schedule. It’s really not hard to pack away a lot of miles if you start walking early and stop walking late.

By midday you can start estimating how much farther you’ll get. Whether or not you want to shoot for that next pass, stop ahead of it, or push for some objective. But a general strategy for me (assuming ~8pm darkness) is “how about around 5:00pm we start looking for a good stopping place, and try to be driving in tent stakes no later than 6:00pm”.
If you’re feeling beat down, go slower. If you’re feeling pumped, push it. Either way you know that (by consulting your map and planning materials) that you’ll have plenty of time for evening and a comfortable place to crash.

Get moving early.
There’s nothing fun about standing around a cold campsite in the early dawn hours. But if you went to sleep at “hiker midnight” (sundown), then you’re probably going to be awake by 5:00am if not earlier. It will be cold and you’ll likely have some ice and moisture on your sleeping gear. Provided it’s going to be a clear sunny day, pack it all up as is. Start eating a cliff-esque bar and get walking. You should have done everything the night before to make breaking camp be a 15-20 minute affair. Keep your trail clothes in your tent/bag/bivy so they’re not ice cold in the morning. Get walking. Sure, it sucks to start cruising at 5:00am but you’ll warm up and have more hours to work with.
By mid day you’ll have been walking for ~7 hours and can stop for a bit. Wash your feet off, maybe wash your whole body off in a stream. Put your wet sleeping gear out on a rock to dry in the mid-day heat. Charge your phone with your solar charger. An hour or so later, get moving again.
Also, mosquitoes tend to be extra-motivated in the hour right after sunrise: you’ll bail on them before they show up and since you’re moving they won’t have an easy time latching on.

June is a rough month in the High Sierra.
Intellectually I knew that June generally brings mosquitoes and high/fast waters. But there’s a difference between knowing something and really having it seared into your memory the way that can only be achieved with the firebrand of reality.
I am a mosquito magnet of epic proportions. It’s truly shocking watching them fly by others and head right to my juicy capillaries. Spring through fall carries mosquitoes in the Sierras but the spring thaw causes water to be nearly everywhere and thus mosquitoes are nearly everywhere. And mosquitoes can make the difference between a nice couple of hours hanging around watching a sundown versus hiding in your tent/bivy as they mercilessly attack your mesh netting.

With all that melt comes the swelling of streams, creeks, and rivers. Bridges can end up submerged. Stepping stones to hop across are equally deep, tossing up whitewater. It’s worth remembering that in our county people die every year from drowning or the trauma that results of getting carried away in a river.
At best, your feet will be getting wet constantly, and if you take your shoes off to cross you’ll be taking the time to do that ~12 times a day.

A benefit to June is that the days are long, allowing you sunlight by 6:00am and not needing a head lamp until nearly 9:00pm (in the Eastern Sierra). For thru-hikers in particular, this is pretty ideal.
You won’t eat much.
My friend and I knocked out 27 miles on our last day. Outside Magazine’s calculator says that I burned roughly 320 calories an hour, so 8,640 calories. That’s a lot, and nearly impossible to eat enough to support. When you’re walking and scrambling all day there’s not a lot of time to eat, and even if you could most folks find their appetite suppressed.

It seems really counter-intuitive but you’re better off with slightly less food than slightly more as you’re probably over-estimating what you’ll eat anyway. It’s of course better to be dead-on accurate but I’d rather stretch my meals a bit than haul a bunch of weight (food) around that I never use.

Figuring out what to eat and how much is a never ending quest. Most folks, especially if only going out for a couple of nights, are generally better off buying freeze dried food (Mountain House, etc) for their dinners. I don’t personally enjoy the stuff and find it expensive, but to each their own.
Be prepared for the long dark.
Winter backpacking sucks for me, chiefly, because of the incredibly long nights. The sun comes up much later, stays lower in the horizon offering up less heat, and sets earlier : the whole “winter” thing.
I generally need 6-7 hours of sleep to feel good, but 9:00pm plus seven hours is 4:00am and that’s if I don’t wake up early or pop up in the middle of the night for some reason.
If you can lay peacefully in the dark of your tent for a couple of hours with your own thoughts, go for it. For me I pre-load my phone with several long and dry audio books. Stuff on moral psychology, political autobiographies, etc.
Try not to think of night time as a cohesive block of sleep but rather a long span of cold and darkness in which you’ll be mostly asleep but also awake for portions.

Filtering water is probably not necessary.
I’ve watched cows crap and pee into a river that I’m getting water out of: you definitely want to filter that. But I’ve also seen snow melt from a 13,000 foot granite spire: you don’t need to filter it.
Backpacking gear companies make a fortune off of selling filters, and it’s hard to argue against the safety-first adage of “well you don’t know for sure that’s safe so filter it to be positive.” That’s true, sort of, but you trust your car won’t explode the next time you go to start it even though you don’t really know that for sure either.
Just read up on the data and make your own decisions. What you’ll find is that it is very rare to find dangerous protozoa (giardia lamblia being a chief culprit) in wilderness settings. What is very common however is people taking a dump, not washing their hands properly, and then grabbing some of their buddy’s trail mix. Further, the incubation period of gastroenteritis (aka “food poisoning” aka “stomach flu” aka “jelly belly”) can be hours, days, or weeks. So one week after a backpacking trip when you come down with diarrhea for a day it’s complete guesswork as to the cause.
If you travel along rivers known for heavy use, I’d bring a filter. If you’re watching snow melt drip off a granite slab, no one’s going to stop you for lugging a filter around and taking the time to use it, but base your decisions in data and not REI’s marketing. To which, I’ll leave you with these conclusions from the linked study:
Published reports of confirmed giardiasis among outdoor recreationists clearly demonstrate a high incidence among this population. However, the evidence for an association between drinking backcountry water and acquiring giardiasis is minimal. Education efforts aimed at outdoor recreationists should place more emphasis on handwashing than on water purification.
But of course, outdoor companies make a lot more money selling you $100 water filters than they do a $3 bottle of Campsuds.

The more you go, the better you’ll do and the more fun you’ll have.
The first backpacking trip I went on was in 6th grade. I brought, amongst other ridiculous items, a propane lantern. Cotton socks and ill-fitting mountaineering boots rounded out the disaster.
Until you know what you need and what you don’t there’s a tendency to bring items “just in case”. The penalty for all these unnecessary items of course is weight which directly corresponds to pain and fatigue which equally tracks with you hating life.
Similar to life in general it takes a while to learn what makes you tick versus what your neighbor is into. You both probably love indoor plumbing, but you might have a better mountain bike because that’s important to you as where your neighbor’s TV might be better.
I’ve seen people in the backcountry with stuff I’d never bring, and I’m sure they feel the same about me. But do try to lock in the general principles and common threads that nearly all wilderness travelers can agree on. Go with other people that have experience and learn from them, I certainly do. As soon as you get back and unpack, note the things you loved, the things that were debatable, and the things that you didn’t even use.
Hike your hike.
Maybe backpacking for you is getting somewhere to hang out and fish for a few days. Maybe it’s crushing miles. If you’re like most people it will be several different things and it will be based on your input and those that you’re with. Don’t get boxed into doing things that you really don’t want to do, but don’t make the world revolve around you either, if for no other reason that you won’t learn new ideas or have your boundaries pushed.

And hey, maybe I’ll see you out there sometime. It’s a mighty big backcountry and I hope you find it as good for you as I find it for me.