I was never really a fan of the LC or the LC II because they were such compromised designs. Apple retired the 68020 with the original Mac II only to re-introduce it with the LC less than a year later. The LC II got a 68030 at the same 16 MHz clock speed as the 68020 in the LC, and the rest of the machine is virtually identical. In order to cut costs, Apple used a 16 bit data bus on both machines, which considerably slowed both machines down, and artificially limited the RAM to 10 MB maximum, no matter if you install larger memory modules.
Both machines had a default resolution of 512x384 in order to get 8 bit color with the 256k of video memory on the logic board. If you install a 68 pin 256k VRAM SIMM, this bumped it up to 640x480 at 8 bit color, which is almost a required upgrade because many Mac applications by this point expected 640x480 at minimum and would refuse to run otherwise, leaving these Macs stuck with older software designed for the compact Macs that ran a screen resolution of 512x342.
The LC III and LC III+ is where things turned around, this was a clean new design that didn't make any serious compromises that drastically affected performance. The bus was a full 32 bits with a faster 25 or 33 MHz 68030 and 512k of onboard VRAM, upgradeable to 768k. I have one of these machines and it's so much nicer. There were upgrades for the LC and LC II that gave them faster CPUs, but the 16 bit bus really limits the performance increase possible.
As for the caps, I would say replace all of them besides the fat line capacitor. I've recapped several LC style machines, including my own LC III in the last couple of years that all were suffering from leaking capacitors. The ones in the power supply are hard to see if they're leaking because it's such a compact design, but once you start pulling caps out of the board, you'll usually see wetness under the caps where the electrolyte is coming out. The same goes for the SMD caps on the logic board, the leaking usually stays mostly under the cap unless the machine is stored sideways, when it will seep out across the board.