(I wish there was a beginner's forum for posts like this one, but since there isn't, I guess "Trumpet Discussion" will have to do.)
These are my own experiences. Your mileage can and will vary, but maybe this will give some readers ideas - hopefully good ones.
I came back to the trumpet two months ago today, when my wife gave me a trumpet for my birthday. I hadn't played (much) in 24 years, since giving up the trumpet at the end of 8th grade (How/why did you start playing trumpet?). (Yes, that makes me 38.)
We'd gone to the local music store in October and tried out a lot of trumpets. I was pleasantly surprised by the tone of an old TR300, and my wife was pleasantly surprised that I still had tunes memorized and could play a wide range. I think that sold her on the idea, and she bought me the trumpet - but of course I had to wait until my birthday to actually play it. In the meantime, she was practicing recorder all the time and advancing quickly, making me kind of jealous!
I used that month, though, to learn a lot about trumpet and about music. I'd never had a broad music education. Basically, my teachers taught me to play the notes on the page, preferably more or less with the people around me to some degree of tunefulness. I had no idea, though, what we were up to, why major scales sounded different from minor scales, how to read bass clef, or how to transpose. So I got some basic music theory books, and Jonathan Harnum's Sound the Trumpet, which finally explained to me what the trumpet vocabulary looks like, how the different parts - many of which I'd heard of but never used - go together, and how to use listening as well as playing.
I also went back and got the method books (Breeze-Easy) I'd used in 4th and 5th grades, and most of what I'd used later. Finally, I figured out where the strange tunes in my head all these years came from, but now that I had more of a clue how music and trumpets worked, I could also see why the exercises did what they did, what the progression was meant to do, and how they built to a coherent whole. You mean it wasn't just pointless homework? That was pretty wild, and still often is, though it's a long ways from reading Arban.
One of the strange things about getting the old books was that they brought back the voices of my teachers. Looking through them reminded me of all kinds of good things and some awful moments too. It also reminded me of various conflicting warnings and teachings, which at least gave me a sense of where to doubt what I'd been taught (and where not to, for now).
When I got the trumpet, I just wanted to play. I knew I didn't have the muscles at all, and that I'd played the test trumpets using unacceptable levels of pressure. (When your front teeth feel loose the morning after briefly playing stuff that only went up to D, maybe E, near the top of the staff, then I think it's unacceptable.) I also knew that relying on pressure was my great weakness when I played before. Yes, you need to use pressure to hit high notes, but I had never properly built the muscles needed to do it right.
I went slowly, staying below C for a few weeks, but Christmas was coming and I played some carols that went higher - and fell back into bad habits very quickly. I stepped back to concentrate on building the basics of my embouchure, and then had an emergency that took me completely away from playing for four days, and after that was definitely back to basics. After a few more weeks of playing scales, intervals, and slurs, mixed with some basic low tunes, I'm using a lot less pressure, even when practicing notes up to G just on top of the staff. I'm a long ways from hitting notes above C reliably the first time around, but that's okay with me. I'll get there, and I'm very glad I backed off for a while, building more slowly to make bad habits less necessary.
(I'm also just plain enjoying playing the lower register of the trumpet (Lower brass), even transposing tunes down there for fun and exploring pedal tones.)
Overall, my fingers seemed to remember everything, my tongue remembered most things (not double-tonguing, though, which we'd never done), and my embouchure muscles had some ideas but no strength to speak of.
There are some extra challenges. I work at home, which makes it easy to pick up the horn, but I still have work to get done... and we have a 10-month-old baby whose sleep is really best left undisturbed. I end up playing in some shorter bits plus a longer practice time in the evening - probably a minimum of 15 minutes during the week and half an hour on the weekend. Fortunately, my wife is very supportive, and glad I don't mind her similar practicing on various recorders.
My goals are pretty relaxed, perhaps even offensively relaxed, for some here. I'd like be able to play the full range I had when I quit by the end of a year playing. That's not too extragant, basically from low G to high G, with a few extra notes around. (I hadn't know then that you can play real notes in pedal tones...) Eventually I'd like to be able to play the full range shown in Arban - which is only a few notes higher. I'm not interested in the squawk book, and while I love the 2nd Brandenburg Concerto, I don't feel any need to play that high myself. Maybe I'll transpose the part down someday for fun.
The high point so far has been a simple eight-measure duet my wife and I played last night. A bit of transposition, a bit of practice, no audience but the baby. Recorder and trumpet doesn't seem like a typical duet (and the baby could have contributed maracas), but it felt just right to us. We'll be doing a lot more of that. I'm also hoping to join a community band, though the one I was hoping for is now stuck hunting for rehearsal space.
For those crazy about hardware, I'll note that I much prefer the 5C mouthpiece. I tried it by accident when testing out trumpets. Other folks tell me I have a richer sound, and it feels much better than the 7C that came with the trumpet. My best accessory purchase was a sturdy Proel music stand. It's a big improvement over an open laptop or a small table music stand, though those got me started. A TM40 metronome/tuner has also helped. The trumpet came with a straight mute, which is fine for now. For Christmas, I got the Pocius Trumpeting By Nature book, which has helped me re-examine a lot of issues as well as given me a lot of non-playing exercises to work with.
I also fixed up my trumpet a bit (minor TR300 rebuild questions) - thank you very much for the advice given here. It plays much more happily now with new springs and the right valve oil.
I'm well-aware that folks here will recommend a teacher, and Ithaca College is right nearby. However, some of us really are DIY and mean it. That doesn't mean I think I can do it better without a teacher. It just means that I'm comfortable with the pace I'm going and the ambitions I've set for myself.
If anyone actually finished reading all that, thank you - I hadn't realized there was quite so much to tell.