A few tips from me:
1) Some mechs, particularily the heavier ones turn faster when fully stopped rather than moving. The Madcat is one of the examples.
2) Heavier is not always better. Armor is just a number that can be decreased by continous fire from one or more sources. Speed is better than any armor because of the human element. Consider that most pilots have at most 50-60% accuracy against moving targets and about 90% against stationary targets.
3) Some medium mechs have a ton of weaponry and some heavies have quite a bit of speed under their belt... those are your best picks sometimes even when facing assaults.
4) Avoid pointless 'i shoot you, you shoot me' battles.. this happens especially between assaults/heavies.
5) Lower speed means better heat efficiency.
6) Press O to override the heat shutdown, but unless you REALLY need that extra shot.. don't.
7) Crouch to be able to tilt your mech more upwards and to aceive faster missile lock.

Use jumpjets in combat more as small thrusts rather then big long ones, and try to time them exactly before the enemies main gun/s finish reloading.
9) NEVER run into a wall in combat.. that most of the time spells death.
10) Don't be afraid to BA-eject. You can still cause a bit of chaos on the field as a BA, especially if you stocked on some extra C8/Infernos.
11) If you're not equipped to fight aero and there might be danger around the corner... don't.
12) Missiles can be avoided by pushing over 100-120kmph in a direction either from their point of origin, either perpendicular to their point of origin. Missiles can also be avoided by jumpjetting at the right time before impact... sure some might hit your legs, but to be honest, rarely will you have leg damage unless the enemy actually wanted it. Best escape against missiles.. cover. As soon as you see the missile sign, see where they come from then try and find anykind of object between you and them. This is simpler then it sounds. If nothing else.. try getting cover behind any mech... but preferably enemy.

13) Don't let autocannons overheat..ever. The downtime kills you more then if you had leaft 2-3 seconds between shots.
14) Aero just seems invincible.. Use LBX/RAC/AC and down they go.
15) Maneouver around tanks and use jumpjets over them. Go for the sides or if nothing else and you're just facing it's front armor, pummel the turret.
16) Vary your throttle to keep your enemy on its toes.
17) Don't be afraid to go in a Raven even when everyone is in assaults... C3 helps a lot. Especially with a Long Tom in tow.
18) Ask for money and offer money to anyone that might need it. If you get that mech you want, and half the team does aswell... it can only spell good things.
19) Don't be so hasty to offer money to people saying they are "banks".. they'll probably appear in a huge Assault not 5 minutes later and leaving the bank empty.
20) Don't upgrade unless you made atleast the cost of your existing mech. Sucks to sell a Vulture just to see that you can't even buy it again, even though you had 50% of the cost made up.
21) Though 2x AC20 or 4x LBL is easy to fire, don't dismiss 2xMBL 2xLBL 2x SSRM. Learn to see the overall damage potential rather than big bulks.
22) Use weapons for what you'd think they'd be used, since the developers probably thought of it before you and managed to put in some bonuses when being used for what it should.
23) Learn your weapongroupings, learn your chainfire command. Stick Flamers/MG's to any and all extra groups.
24) Testfire your groups before going into battle.
25) You can steal enemy mechs if you blow up their cockpit.
26) Repair in the mechbay by powering off with P in the center of the individual mech bay.
27) Sell your current mech with J while in the center of the mech bay. Don't repair before you sell since damaged mechs already loose value.
28) Co-operate with your team-mates by assisting them and don't be afraid to act first. Make yourself the middle of the battlefield and you'll have allies around you.
29) Use initiative. Get in a hovercraft and guard two capture points. You'll do more for your team liek that rather than getting another heavy, walking it for 4 minutes to the battlefield, then quickly dying.
30) I'm up to 30 hints... i should stop now.
I'm done for the night...
