From what I've gleaned:

You gain stats from:
Your level base stats
Your rank
What you have equipped
Your girls stats
X best pieces of girl equipment you own for each category, where X is the number of girls you have.
So if you have 10 girls and you buy 10 of the best car, you get the stats from all 10. If you buy additional best car or lower quality cars, it won't improve stats until you get as new girl

At least as far as I've gotten, stats seem completely pointless if not counterproductive. Your random selection of opponents seems to be based on your stats, and if anything, their stats increase faster than yours do... not that it seems to matter much, whether you win or lose seems completely random, if not simply based on how much you've won recently. Seems like when I get home from work/wake up I have a good chance of winning against anybody, as I keep fighting I stop being able to beat anybody. And, unfortunately, when it comes to collecting individual items to upgrade girls, what you actually get seems to be 100% random, if not actively biased what you need. Every single girl I need to upgrade (like 11 of them) Need either a ruby watch of glamour watch (or both) to upgrade. Pretty much all the other objects needed are in the double digits. Haven't gotten one of either since Monday. Every other item they need has 9+ copies.