Definitely read the guides and stuff on the wiki, they're pretty good:
http://gearhead.chaosforge.org/wiki/index.php?title=GearHead
For mecha, the #1 skill to pump is piloting - if they can't hit you, gives you time to hit them. Then yeah, pick one of the distance skills - at start gunnery because the big weapons are harder to come by early. Also very important is initiative, awareness and spot weakness, then electronic warfare later when you get some ECM.
Also, even if you don't attack with them, "Mecha Fighting" is used to parry with your shields, and "Mecha Weapons" to parry enemy physical attacks, so don't completely neglect those.
Mecha repair is a good source of cheap xp early on. Mecha engineering is very important to get your mech optimized.
I personally have been starting most characters with maxed (15) reflex, speed, perception and knowledge, the other stats average, and low (7-10) charisma (why talk when I can shoot it

) I pay cash to train skills wherever possible, saving xp only for stat boosts and talents.
That Corsair is a pretty good mech to start, but you gotta get that MV and TR back closer to 0 especially early on when your piloting ain't so great - those -4s on your screenshots will be fatal. Dump your extra crap in town so it doesn't weigh you down. Later I use a cheap mech to keep my extra stuff in, so it doesn't clutter up the screen. Definitely take out the Corsair's heavy wheels, and stick in the best sensors, targetting and ECM you can buy - keep looking for upgrades there. Also keep your eye out for good light long ranged weapons. Until then, the Shaka Cannons are not too bad at all - but watch your weight.
I like to stick on a few personal scale weapons - bazookas/rapid fire bazookas give you something to do while waiting for your big guns to recharge. Early on the ammo is kind of expensive though. Sniper Rifles are cheap but shorter ranged, and I like a few shotguns (esp auto-shotguns) with shard ammo to strip off armor at close range.
Yeah, Mecha-fu is hard - you need good piloting, good Initiative, and a fast maneuverable mecha. And even then when you hit it will damage your own limbs

So it's best when you build up your mech for it - add extra legs and arms.
On the ground, same idea - Dodge is nice, pick one out of Small Arms/Heavy Weapons. Later don't neglect Armed Combat (used to block with shields). Watch your weight, it's easy to get overloaded. Martial Arts is OK secondary, but it's a bummer closing with enemies, so you really need a ranged skill first.
Tips to keep from going nuts:
-make lists of peoples names and keywords, especially shopkeepers, and guys with jobs like leaders, guardians, etc. Then you can use your phone to call them in the city to check prices/look for jobs, without having to spend a ton of time walking around and chasing them down. Keywords work in the phone too (the title under the portrait like "leader") so you can phone that way if you forget a name.
-make lists of shops, to really upgrade the mecha I tend to keep making the rounds of the good shops looking for those top level parts. The absolute best stuff is salvage only though.
Heh don't get me started, I could babble on for pages and pages
