I have a couple of rescued White clouds in my (large) goldfish tank. They are great little fish - very active and pretty as well as being hardy and happy in cold water. You can sometimes get a "gold" version as well which have a bright yellow body and red flashes on the fins. I'd definitely recommend them as an alternative to goldies - they grow to about 2/3cm whereas bog-standard goldies should grow to around 20cm - that's why they need such a big tank.
With White clouds you can also have real plants in the tank if you want (my goldies chomp everything except moss balls!).
Although small fish don't need the same volume of water, it's worth bearing in min that a larger tank is MUCH easier to look after. Small bowls / tanks will need a lot more cleaning & checking water quality etc.
A good start for any prospective fish keeper is to find out about " fishless cycling" (google it!) and buy a proper water testing kit.
The easiest way by far of setting up a new tank is to grab a chunk of nice scummy filter sponge from a healthy, well-established tank and stick that in your new filter. But if you don't know anyone with a tank you can build up your bacteria by adding ammonia and testing, or do what I did with my first tank and cycle it using fish food bagged up in old tights. Takes about four weeks.
DO NOT trust a shop which tells you they will "test your water" from the tank before it has any fish in it and then try and sell you more than one or two fish at a time.
Fishkeeping is a fantastic hobby especially for geeks like me but be prepared that it does involve regular work, especially at the beginning!