Instead of single fights, it's better to watch a fighter's entire career. You get to see how they develop from one match to the next. You kinda want to avoid UFC heavyweights, they have some decent match-ups here and there but overall they tend to be the least competitive weight class. (might have something to do with the 60lbs weight variable)
You should also know that the fighting may look chaotic at first, but it's really very simple. All combat can be defined by three aspects: striking, grappling, or submissions. Back in the early days of MMA the fighters were all one-dimensional, and it was just a clash of styles. Now every fighter in the top 5 of every weight division (except maybe heavyweights) are expected to be able to win with at least two of the three, and be proficient enough to defend against all three. The real differences in performance are seen not just in a fighter's ability to use any given aspect, but also to transition between them. This is a principle that Bruce Lee promoted, and you can clearly see the template of modern MMA in the
opening scene to Enter the Dragon. I'll just list the most obvious names you should familiarize yourself with, wiki pages have their career history, and you can go search for fights on youtube or something.
http://en.wikipedia.org/wiki/Forest_Griffin
Like a lot of people, the Bonnar vs. Griffin match in 2005 was the time when I got into the sport. The heir apparent to Couture's legacy, not that great of a fighter, more of a "hard worker" than a "genius" type, but fun to watch nonetheless.
http://en.wikipedia.org/wiki/Lyoto_Machida
Currently my favorite fighter, Lyoto Machida. Some used to call him boring because he specializes in evasion and has the patience of a 70 year old man, but that's just smart fighting. The only Karate specialist to see real success in the UFC, he is okay at grappling and submissions, current title holder in UFC's light heavyweight division, and currently the only title holder to have a flawless MMA career.
http://en.wikipedia.org/wiki/Anderson_Silva
Anderson Silva has been considered the top pound-for-pound fighter for years, undefeated in the UFC, and title holder of UFC middleweight division for several years. A classic example of a fighting genius, his fights are like how-to MMA demonstrations. He will be retiring when his UFC contract expires.
http://en.wikipedia.org/wiki/B.J._Penn
Youngest person to ever get a blackbelt in BJJ (at age 16), kinda crazy and a jerk, he is the current lightweight title holder. Another fighting genius, a real contender for the #1 p4p honorary. Back when Matt Hughes used to be the undefeated UFC welterweight title holder (division above lightweight), BJ Penn went up and took the title from him simply because he wanted it. Almost all of his loses come from decisions or his utter lack of physical conditioning, although he's spent the last few years changing that.
http://en.wikipedia.org/wiki/Georges_St-Pierre
Another "hard worker", he's had a pretty stellar career in the UFC. However, this is tinged by the fact that he's much bigger than almost all of his opponents. He is very skilled, however, as he trains with a number of top-level fighters from various weight divisions as well as various Olympic teams, plus he trains all year every year rather than simply training for specific fights.
http://en.wikipedia.org/wiki/Randy_Couture
Legendary hall of famer, multi-division, multi-time champion. He's come out of retirement twice and gone on to win titles both times. Probably the nicest guy to ever pound another man unconscious for money, I recommend not just his fights but also his interviews. Started as a Greco-Roman wrestling specialist and is considered the godfather of ground and pound, was one of the first prominent fighters to learn other aspects of fighting well enough to contend with other top-level strikers.
http://en.wikipedia.org/wiki/Wanderlei_Silva
Wanderlei was a really big name back when PrideFC was still competitive. However, UFC fighters perfected the art of weight-cutting, so natural heavyweights now fight as light heavyweights, natural light heavyweights fight as middleweights, and so on, which puts him at a size disadvantage. His victories are generally KO's and ref stoppages, and he owns some of the most spectacular knock outs ever caught on film.
http://en.wikipedia.org/wiki/Andrei_Arlovski
Andre was one of the only heavyweights I respected in the UFC, I was sad to see him go to Affliction. Master of Sambo fighting, which itself is a crazy gotdang sport. The only fighter in the UFC that really had his number of Tim "The Jab" Silvia, who beat him twice. There's an unwritten rule in the UFC, which is best-of-three, and then those fighters simply don't fight each other again. Once Tim beat Andre for the second time it pretty much locked Andre out of title contention for as long as Tim held the title. It was during that time that he decided to move on to other sporting circuits.
Between all of those fighters you should run into nearly every other important name in MMA.