I started with a 29g as my first tank as well!
I had lots of fun stocking it, personally some of my favs are Aphyosemion Australe (Lyretail Killifish) and Harlequin Rasboras. They are both fairly hardy fish and fun to look at as well. The Killifish can be a bit hard to find and run a little high in price though. Other fish you might want to take a look at are Fancy swordtails, Guppies, Red Cherry Shrimp, Mollies, and Platies. A 29g can also hold a single bristlenose pleco which is a neat fish although you need to feed them algae wafers and give them a source of driftwood.
Some fish that are touted as beginner fish that I would probably avoid are both tetras and Danios as every experience I've had with them has been negative because of both aggression and fin nipping. But other people love theirs and have never had a problem, so it's probably just bad luck on my part.
I ran an Eheim Ecco 2234 on my 29 because I had it seriously overstocked when it was running but that filter helped keep the levels in check. As far as affordable filters go, you might want to check into a sponge filter I've always had a lot of luck using them.
I find tank size rating on filters to be complete junk, so I would try to find a filter for about a 50g tank or so on a 29 but it depends completely on what you are stocking the aquarium with.
AqAdvisor - Intelligent Freshwater Tropical Fish Aquarium Stocking Calculator and Aquarium Tank/Filter Advisor
This is a good site to get a general idea of what numbers of fish to stock in your aquarium as well as a filter that is strong enough to support the bio load.
What are you using as an ammonia source for cycling? Cloudiness is very very common in new tanks, it is usually just a bacterial bloom. They are almost always completely harmless to fish (Cyanobacteria blooms can be dangerous but that's not what you have) I find they will run their course over a week or so and then go away.
Finally, Welcome to the fun of fish keeping