Are you kidding?!? The Cubs don't sell tickets to real baseball fans.
As far as getting to the Dome, you should have no problems with tickets. The last couple of years, even with the Twins doing well, I've been able to get seats behind home plate the day of the game. Plus, it's the cheapest ticket you'll find.
Try not to get seats anywhere outside the infield. This stadium's seats are positioned for football and you'll get a kink in your next trying to watch the action down the left and right field lines.