Name and Equipment on Cores

I use head:most expensive
core:the most heaviest
legs:the biggest 2 leg style costs 64000
Arms:most armoured and heaviest
Weaponsowerful laser weapon costs 75000
moonlight
laser cannon on the back along with the best radar
best FCS,generator,boosters

Here's what got me through most of Armored Core, the origonal, as soon as I got all the parts I needed.

HD-9066 (The humanoid one with the slit eyes)
XCH-01 (HEavilly armored core with the bubble back)
AN-K1 (Best arms, just ask 9ball!)
LN-501 ("Cowboy" legs because the feet look like boots)
GBG-10000(Best output, recovers better than the gold one)
TRYX-BOXER, or QUAD (Depending on mission, extends FCS size without sacrificing range)
B-001 Extremely lightweight yet has decent efficiency.

You might notice that there isn't much room for weaponry, but that can be tweaked in by switching out the AN-25, and the HCL-01 for more weight allowance. In that configuration, it'll carry the KARASAWA, and a light sword, or a lighter hand weapon with some missiles. I usually carry one of the energy rifles because they don't cost anything to fire. A cheap MG is good for anti-aircraft, my preferrance is the MG500.
Good ground speed, manuverability, and flight time, but with decent armor, and sheilding. I basicly picked parts for their ballance of stats, and weight. Making the changes above may net you more carrying capacity, but you'll lose survivability with the lower defenses.

Like anyone who's been playing this a while, I've got lots of designs, and a few favourite parts. Generraly, when I have enough credits, I just buy all of these, and stay out of the shop unless I need something special. This allows me to retool for each mission rather painlessly.

Heads: My fave is the 9066 because it's light, but with good sheilding and armor. It also looks real cool. On the down side, it's also high drain, so I'll usually swith out for another if I'm worried about having enough energy.
Seccond place is a tie between the ONE, and RADAR. The former is low drain, and has a good range, but the latter is high drain with the best of any head in the game. Neither has decent sheilding, though.
Arms: As far as I'm concerned, thes serve as extra armor, and sheilding in adition to their weapon carrying capacity. I like them light, so it's always a toss up between the AN-25s, and the K1s. The first are the lightest in the game, and have a little more armor, while the latter are better sheilded. I usually go with the K1s unless I'm slimming down to stay under weight.
Weapon arms: Best used on quads, and tanks because they cannot use swords. My favourite is of course the plasma cannon which can melt damn near anything, including you if you get too close. I'll use the MG25/2s for VS, but it's not as fun in this version. The AW-30/3s are the lightest in the game, which is good for making a cannon toter with something on the shoulders.
Cores: Just going by the numbers, the HCL-01 "Bubble Back" is the best. I'll use the lighter one to cram in Options, but I'd really rather have the defense of the heavy one. The stock core is complete garbage.
Legs: First off, I like RJs. They're manuverable, low drain, and can jump phenominally well. On the down side, they have nearly no defensive value, so I usually use the heavy core (above) to compensate. All other stats, speed, capacity, and armor, are about the middle of the road. I like the LBKS-2B45A best because they're the fastest, and best sheilded.
Homopoid(LN...)- Basic bipeds, the 501s have the best stats. While there are faster ones, they're really not that much quicker, and don't carry nearly as much. For heavyweights, I go with the 3001C("Adidas" legs). Again, there are heavier ones, but these are more stable, and kneel quicker.
Arthropoids(LF...)- Fast, and stable, they can fire cannon on the go, and back up at full speed. I really don't see any reason not to go with the lightest, or the heaviest. They've got the best stats anyway. I will warn you that they can't use swords that well. Tte catipilliars(LC...) are pretty much the same, but slower, and without jump function. I hate them, and only use them when I want to save money on the booster.
Internal parts(Generators, FCS, and boosters) Rarely change, I use the GBG-10000 exclusively after the first mission because it recovers quickly, and has the most power. Boosters are always either the B-001, which are lightest, and the B-P351 which are the most efficient. FOr FCS, it really depends on weaponry, and mission. The TRYXs expand the window without shortening range, so it's usually one of those. I'll use the QX-9009 only if I'm carrying nothing but wide/shallow weapons, and I want more range.
I'll get back to you on weapons, because that promises to be a long post by it'self.

Basically my multi-ppurpose design, it does just about everything reasonably well, but none excellently.

HD-RADAR (Best range)
XHC-01 (Good Armor)
AN-K1 (Best Arms.)
LFH-X5X (5000 WPs!)
GBG-10000(Best Generator)
B-P351 (Efficient)
TRYX-QUAD(Solid gun)
WC-01QL (Plasmatic death)
WM-PS2 (Triple Missile)

A generalist can beat any specialist by not playing their game. This design has good speed, armor, firepower, and most of all versatility. It doesn't fly good, though, and is weak up close. The latter, though is a lure for those bladers, because I can back up almost as quickly as they can chase me, and get several rounds of MG into them. The Plazma cannon is great for sedentiary tanks that can't dodge, or handle the energy. The missile is primarilly anti-aircraft, with the MG pulling double duty. There's no sword, because I don't play REBEL, and the wave sword is in MOA.