Nix the saltwater idea, you'll find freshwater plenty challenging. Not to mention about a gajillion times cheaper (though still a wallet denter).
As far as specific recommendations go for things, get a submersible heater and a good one, too. Your heater is one of the most important pieces of equipment, so don't pick the cheapest option (there will be other times when that can be appropriate).
By the way, I am assuming you'll be wanting a warm freshwater tank. Cool ones are an option you should be aware of (and don't require heaters) but they limit your fish options to pretty much goldfish, and goldfish, which produce a lot of waste, require extra filtration and a larger amount of space per tank (ie, you could only keep three or four comfortably in a 29 gallon).
Filters usually move water without needing additional parts, so I don't think a water pump will be required. You might consider an air pump with an airstone to add some bubbles (and thus oxygen) to your tank, though this isn't nessecarily a requirement.
As far as filters, don't get an undergravel filter. They're a bit like spandex or communism: they seem like a good idea but just won't end up working out. Canister filters are nice, but are more high-end and require a bit more expertise with filtration. Good, layman-friendly filters can include powerfilters (which usually hang on back of the tank and have cartridges you can easily replace).
Some basic questions to help you decide what filter is best for you:
Are you familiar with the three types of filtration (mechanical, biological, and chemical) required to maintain a tank? Different filters address these three components differently. The biological component is very important, as this refers to the bacteria you need to have in your tank to convert toxic fish waste to a non-toxic form (gaining the bacteria is known as "cycling" a tank, something vital to having fish but often unmentioned to newcomers to aquariums).
Also, what kinds of fish are you looking to keep (or have you decided)? Some fish have different needs regarding filters (mostly in relation to the currents produced by them).
You should keep in mind that in the beginning, you won't want to have a planted tank, since plants, in most cases, open a whole other (expensive) can of worms with CO2 injection, appropriate lighting, and fertilization. For your first tank (or at least the first while you have), you'll probably want to stick to fake plants. Don't be disheartened, though, some fake plants look great.
For now, I recommend you read, read, read every bit of information you can find, and research every choice you make before you go through with it. Don't rush into anything, as that is a sure way to find disaster.
Good luck, though, and welcome to AA!
Welcome to AA, jarnism! 
