Well, the most common instruments to find at a modern Irish tune session these days are certainly fiddle, accordion, Irish wood flute, tin whistle, guitar, bouzouki, mandolin, concertina and maybe a bodhrán (the round Irish drum, played with a tipper). Some of the less common but fine-sounding additions might be banjo, bass, hammered dulcimer, keyboard, uilleann pipes (that's pronounced like ill-un, BTW), or Irish harp, which I play. Your friend's cello would probably sound really good with the session.
I wouldn't recommend a trumpet--brass instruments would be too loud to play in a session and would drown out the other players.
As far as music, the best site I know is at www.thesession.org, which is a huge compilation of Celtic music and notes about the tunes. For books, the one that most Irish musicians like to refer to as "the bible" is the 1905 tome "O'Neill's Music of Ireland". I like the unabridged version, which has 1,800 fiddle tunes, with the titles in Irish as well as English; but the more common abridged form of the book has only 1,000 tunes! The abridged form is available in most music stores, in the edition edited by Miles Krassen. The books are good for any Irish musician, not just fiddle players--we start with the melody line, but we all add our individual ornaments to the music--each musician plays the tune just a little differently, and that's one of the signatures of Irish music.
Do you have a local session in your town, perhaps at a local pub? Irish musicians all know that you can't pick up the music just by reading it from the page--you have to hear it. It's like learning a language--you learn best if you hear it spoken by a native speaker, otherwise you won't get the accent and inflection right. I'd suggest talking to some of your local Irish musicians; maybe some might even be willing to give you lessons. But by all means, go and hear the music live. Ask them if they'd be okay with you recording the tunes, just for your learning; most session musicians are okay with that, because that's the best way to learn them. I'm pleased that you want to learn the music; one of my greatest joys is sitting in a roomful of Irish musicians, with a fine pint at my feet, and playing tunes half the night or more!
You are welcome to e-mail me if I can be of further help.