Logistics Officer reporting for duty, Sir!
Rifles indeed suck. Grenades can be more useful early on, since getting recruits with a high Throw skill is easy and if they don't have any other useful stats they're really expendable. A rookie with a grenade and pistol is a good way to scout for aliens. If they don't have time to prime and throw the grenade, you can shoot with the pistol. Occasionally, it even kills an alien. If they can throw the grenade first, you're in pretty good shape. Just remember the explosives WILL destroy equipment on the ground, so be careful about spamming an area with grenades too much. Don't want to destroy those valuable Heavy Plasma guns!
Any Strong characters (60+) should probably be given Autocannons. They're much more useful then rifles and while they are expensive. Oh, and remember that characters gain stats for anything they actually use, so giving a character a heavy load will raise their strength. Useful if you have a promising recruit with great stats but a moderate strength, since they'll only be slow for a few battles.
Research tree suggestion: Laser Pistols, Motion Sensors, Alien Alloys, Personal Armor, Laser Rifles, Medic kits. Laser pistols aren't as good as laser rifles, but better then normal rifles, and the armor will help a lot. Oh, and don't bother with the Heavy Laser. It's pretty much worthless (except to make and sell, where it gives a good profit).
Build up a decent research section ASAP. I usually have two research groups. One (large group) doing my primary research, and another working on something I want a bit less. Having them all focus on one thing is also a good tactic.
Selling off alien corpses is also wise, as you only need 1 of any type to do research on. You get a few every mission and they sell for a decent amount.