If you want to start in Prague and end in Budapest, it's easier to fly into and out of those airports, all on one ticket, even if this means changing planes. To find these flights, use the "multi city" rather than the "one way" or "round trip" option on Kayak or airline websites (including United's). Do NOT look for two one way tickets, as that's usually much more expensive.
Put in Atlanta to Prague as your first segment, and Budapest to Atlanta as your second segment. See what options you get. You may well have to change planes on one or both legs, but that's easier than arranging surface transit on arrival. A big problem with the Munich to Prague segment is that if you buy advance tickets at a discount, they're not refundable or exchangeable (or minimally so), so if your plane is late and you miss the train, you're out the money. If you wait to buy tickets until you arrive, these can be expensive. However, if you are flying these segments all on one ticket and the arriving plane is late, the airline is responsible for putting you on the next available flight at no extra charge.
If you've already booked your flights for this trip, remember this for next time, and let us know, so people can help you get to and from Munich (not particularly fast or cheap, particularly for the Budapest to Munich portion). In fact, if you've already booked round trip to Munich, see what it would cost to change the ticket.