Car hire is generally expensive. The train from Vienna to Salzburg takes less than three hours, leave on average once every half hour.
ÖBB: Get your ticket in a machine before boarding (ca euro 5o each way) ,
Westbahn train (a private company, fares much lower, leave every hour or so, buy ticket on train; Euro 25 each way (but not clear about where they stop in Salzburg, but the staff will help you.).
Salzburg Budapest - there are ÖBB direct trains every two hours. Cost not clear (you can't order international tickest on the net), journey time 5 3/4 hrs
Bratislava: From Vienna about an hour by train, a little longer by bus. There are two stations in Bratislava, one at teh grotty end of town, one more central; you want Bratislava hl st and not Petrzalka. Budpest Bratislava is very slow (and usually involves lots of changes).
Salzburg is pretty but snooty, Vienna a great city (get out to the vineyards for a glass or three of wine on tram No. 38, for instance), Budapest is worth a couple of days, Bratislava about a day.
Hope that helps.