Welcome,
There are hundreds, even thousands of available tartans and there is no actual "right" to wear them (with a few exceptions) but some choose to only wear their clan/family one, whilst others choose ones they like, it's up to you and your personal feelings. I have several family ones I wear but I also wear others whihc I like because of the design or colours , but both are equally valid. It's generally a good idea to find out a little about the tartan so you have an idea of the background but it is unlikely that people would particularly outraged if they saw you wearing their tartan, most likely they would be honoured!
Obviously the most important part of the outfit is the kilt, they come in a huge range of prices, styles and qualities so you need to work out sort of budget you need to put aside. A properly made kilt will last for decades so it is worth investing well.
Most tartan come in colour variations :-
Modern - usually stronger or bolder colours,
Ancient - usually faded colours
Hunting - usually with more blue and green
Weathered/Reproduction - usually more browns and greys
work out the kilt first and then find things , and remember that a kilt can be worn in many way from the very casual to the very formal and everywhere inbetween, it's not jsut for Burn's Night!