HeroClix has definitely gotten overly complicated through the years, and earlier figures are just plain incompatible with more recent figures. Back in the day when most characters only had one figure there was a ranking system that affected point value, and ability scores. One of the many things that HC inherited from Mage Knight. But eventually they moved towards characters having multiple sculpts in various sets with wildly varying stats/abilities.
The real fun part of Modern HeroClix is just how many properties have had sets, and how for the most part they're all game legal. If you want to see who would win in a fight; Frodo Baggins, Ezio Auditore, James T. Kirk, and Wolverine VERSUS Batman, Ryu (From Street Fighter), Hulk Hogan, and Master Chief. You can just do it.
I've never played solo myself, but here are a few helpful links.
HC Realms thread on playing solo (The forums in general are very helpful for new players.)
A simple guide to solo play for general battles (Will require knowing the general rules.)
Custom Solo Scenario (It's X-Men themed but you can work around that.)
Hopefully these will help a bit, it's a war game so it's designed for competition but it's been around long enough that there are both official, and unofficial solo play styles.