I think further explanation is necessary.
Westbahn is a private rail carrier that operates train service between Salzburg and Vienna. These are exceptionally nice trains with free wifi on board. For Westbahn, you buy your tickets on board the train from the conductor, from Tabak shops around town or online - all for the same price. There is no Westbahn ticket counter at the station. Clearly, for a tourist, buying on board is the most simple.
When arriving at the train station, you simply board the train (there is 1 per hour) and find your seat. You don't need to "guarantee seats" - this isn't like airline travel, no one is checking you in; there is no "gate", etc... Just get on, find a seat. If you want to be sure to sit together, then arrive early. As the train originates in Salzburg, it sits on the tracks for a while before departing. It is rarely (if ever) full. Westbahn tickets cost 25 Euro per person.
OeBB is the national rail carrier of Austria and they also offer rail service from Salzburg to Vienna. You can buy your ticket for OeBB two ways - 1) the online purchase of a SparSchiene ticket which will cost 19 Euros (but these are limited in number; once these sell out the next price group will be available, etc; buy as soon as possible to ensure the best fare, in other words, don't wait) or 2) buy the ticket from the train station once in Vienna and plan to pay about 2-3X what you would have paid for a SparSchiene ticket. As with Westbahn, you just get on the train and find a seat. You can pay a couple of extra Euros for a seat reservation, but this is generally very unnecessary. Second class is very nice; first class is not necessary.