An audioquest antistatic record brush will go a long way. They are only about 15-20 bucks. Most of what makes a record dirty I have found is playing them with the slightest amount or dust on them. The dirt gets into the grooves from the stylas. The audioquest brush is very effective in removing all of this surface dust before it gets into the grooves.
Also, the discwasher D4 wet cleaning system is moderately effective at removing dirt. It is the most effective short of soaking the record and actually scrubbing and rinsing it. As a plus, when and if you do get into that territory, of cleaning off of the tt, the d4 brush is a good scrubber if you do want to soak and rinse them. This may give you a little practice before you go buying a bunch of record cleaning devises.
There turntable you have IS a real turntable. It may be inexpensive, and a long way from state-of-the-art, but it will properly play your records, and will sound good. It is capable of good sound, and should sound as good as a cd player in the same price range. It will still do some things better. It should also be as safe to your records as anything.
The issue of cleaning records is something we all have to deal with, no matter how sophisticated our turntables are. We all still get the same benifits, and the same hassles.