We recently just started tracking DI's for my band. This was my first DI experience, and I learned alot of lessons (most of em the hard way)
1) New strings
(If they're older than 2 hours before I start tracking I restring - when we first started tracking our guitarist said "it's fine, they're only 3 days old". Next time we tracked they were strung right before we tracked and the difference was night and day. It's at that point he stopped arguing with me with recording issues)
2) Fresh Battery (A dying battery will make your DI's sound TERRIBLE)
3) Use a Nice DI Box (your countryman is fine)
4) Get a good preamp unit, the best you can afford, you are not going to get that "Pro" sound otherwise (The Profire series seems to be often recommended around here, the 610 model is very reasonable priced, but there are other good models out there)
5) Another thing that gets overlooked is a decent power conditioner. If you are getting alot of AC or EMI noise in your DI's this will really affect the quality, especially if you use alot of gain.