It sounds like you are looking more towards a miniatures type skirmish game or board game. You have a figure representing a member of your team, each fig has a limited number of stats (attack, defense, ranged attack, morale, etc.) so there's not a lot of bookkeeping.
One player takes on the task of controlling the 'bad guys' and perhaps lays out the playing field as it is explored by the other players. In the end the players confront a tough end fight and then get some dice or exp or something to make their surviving pieces a bit stronger for the next session.
There are several games like this out there already, some are out of production but are worth a search of ebay for. In the fantasy genre, their's
Heroquest. Originally by a company called Games Workshop, they sold the rights to Milton Bradley, who massed produced the game in the 90's. It's a modular dungeoncrawl, with some Gauntlet like playing pieces (wizard, warrior, dwarf, etc). The game master can even create little stories around the games if he wishes, or it can just be played for the fun of it.
GW also gave Milton Bradley a space version of the game called
Space Crusade. This was a fun game that pitted Marines against Chaos (evil) Marines. A lot of cool stuff came in the box, that's for sure.
There was another space/horror game called
Mutant Chronicles:Siege of the Citadel. An introduction to the company's (failed) miniatures collection, this boxed game came with everything you need to pit the houses against the legion (zombie marines).
There are some more skirmish games, more recent but still out of production. Games Worshop created
Necromunda, a battle game that pits two players small collection of figs against each other in a giant, rusted cityscape. The gangs gain experience, and suffer injuries, collect artifacts - so there is a sense of advancement and cause/effect.
Mordheim is the fantasy version. Rival gangs fight in a ruined city that has recently been hit by a meteorite. The meteor's slag has magical, dangerous power and is valueable. Once again, the teams gain exp, lose members, find equipment between games.
Both of those games are not played on a board. They use terrain and cardboard buildings that come with the box set, or the players create.
Lastly, there are the recent collectable miniatures games by Wizkids. Mageknight, Heroclix, etc. I am sure you've seen them. The nice thing about these is the stats are all found on the figure's base. When the unit takes a hit, you click the base and the stats automatically reflect the injury. These minis come prepainted (rather basically). The games are collectable, meaning you don't know what you've got until you open the booster pack. You can find online resellers if you need to find certain figures.