Hi there, welcome to the forum and to fishkeeping.
Forgive me from deviating from your question but there's some important stuff to learn before you worry over what fish to get. Sometimes people don't ask teh right questions because they don't know that they need to know the answer!!!
The first thing to consider when keeping fish is the water, a wise man once said 'we are not fishkeepers, we are water keepers, look after your water and the fish will look after themselves'. Now it's not strictly speaking true, you iwll need to feed the fish and such like but the spirit of it is correct.
The single most important thing to learn about in fishkeeping is the nitrogen cycle, this is a bacterial process where the filter breaks down the fish's waste and stops the water from becoming toxic. There's two topics you should read about this which will explain the basics of water chemistry, both are linked in my sig, the first is 'whats cycling?' the second is 'fishless cycling'.
The first will explain the process, how a filter works and why when you first set it up it can't handle the fish's waste straight away, the second shows you a process where you can simulate fish's waste in the tank by adding pure ammonia, this gives the filter a chance to get up and running so that it can process the fish's waste by itself when you do come to add them. Have a read of both of those topics and post back with any questions that you have from there.
Now onto fish selection, you seem to have some terminology a little muddled up here so lets clarify
there's two main factors which divide fish into groups, the temperature of the water and weather it contains any salt.
So you get the following 4 main groups
Cold Fresh Water - room temp water with no salt added, this is what goldfish need and is generally referred to as 'coldwater'
Warm Fresh Water - water around 24-26oC with no salt added, this is what most of the small colourful fish you'll see in the shops need and is generaly referred to as 'tropical'
Cold Salt Water - this is very rarely used but if you wanted to keep fish and inverts that live around the coats of the UK this is what you'd need. There's no common name for it as you don't see it very much.
Warm Salt Water - warm water with salt added, this is what you'd use to keep corals and reef type fishes from the sea such as clown fish AKA 'Nemo' - This is commonly referred to as Marine.
I think what you will be aiming for is warm fresh water, there's a lot of variety and colourful fish and it's relatively easy and inexpensive (compared to salt water which needs a lot more equipment and knowledge.
There's no reason why you can't start out your first tank as a marine tank, however most people don't because it costs a lot more, you need a much greater understanding of water chemistry and it's a lot less stable which means it's not very forgiving. If you make a mistake (which we all do, especially as beginners) with a tropical tank you'll often be able to rectify it fairly quickly and easily, with a marine tank you can find the whole tank crashes and everything dies.
So if you want to do it then by all means do, but leave your wallet at the door and prepare for some reading!!!
Assuming you do want to go with the tropical option then have a read of the link in my sig 'step by step guide to setting up an aquarium' it'll talk you through all the equipment you need, how to choose it, where you can save money and where to spend it, a bit of a shopping list of other bits and bobs that you'll need, it's also got links to loads of other useful bits of info. It's a bit of a long read so get a cup of tea but I think you'll find it invaluable.
There's a link in my sig about fish compatibility which will help you work out what fish go with what, it doesn't give examples or tell you what to get but it tells you how to work out if two fish that you like can go with each other. I'd advise you to take a trip to your lfs (leaving your wallet at home!) and write down the names of everything that you like, come back here and post up your list and we can help you shape it into a sensible stocking list.
OK I feel I've waffled enough there, just to say well done for coming and researching before leaping in and buying fish, you're definately doing this the right way around and with a little research we can get you off the ground and with a lovely sucessful easy tank!
