Been a while since playing ME1, so going off old memories here! I love the infiltrator, but that's what I tend towards. You still definitely need a close-range weapon, and while the heat system can get you into trouble sometimes, I do like not having to worry about running out of ammo in the middle of a huge fight! Later games balance the weapons you can use better, so you can load up with a sniper rifle and an assault rifle, giving you good choices for both options.
Yes, if your teammates have grenades as an option, they do sometimes use them. I never worried about micromanaging my fights, though. I learned who will do what (such as some characters running out into the middle of things) and worked with that. Makes fights a lot more fun as your teammates aren't useless on their own.
For gear, you don't have to equip everything you find. Most stuff you can get at stores later in the game, and there's lots of gear combos that are effective. Just go with what looks the best of the gear you have and can buy at a time, and you should be fine.
Save often and in different slots. You may want to go back and redo some things later in the game. But don't worry, the ending is pretty epic!
Also, the Mako is fucking hilariously awesome to drive. And fly off mountains! I always got the feeling that when my Shepard was going out in the Mako, the other teammates would rock/paper/scissors and the losers had to join her. There's a lot places you'll have to drive around in, but also a lot of places where you just run around and explore planets. Talk to people and do a lot of random side quests; it's really interesting how some of those will show up in the other games. Nothing major, just odds and ends and some neat flavor text type of stuff.
Edit: just remembered his name, make sure you talk to Conrad Verner at the Citadel. No matter what your responses are, make sure you do. He does show up in next two games, but only if you talk to him in each game. He's entertaining comic relief later in the series, so for amusement's sake, talk to him.