Trains On own to Budapest, Vienna, Prague, Salzburg and Munich

— is there one train pass that we can purchase to depart to each of these locations?

Not really , it will almost certainly be cheaper to buy normal tickets for each of your 4 trips (like the locals do), but buy in advance (2-3 months) to get big discounts.
For lots of good info, how to get times and the best way to buy tickets, go to the seat 61 site: https://www.seat61.com/
Under "Train travel within Europe..." you can select each of the cities where your 4 train trips start.

— is it worthwhile to purchase 1st class to be sure of seating and ease of storing luggage?

Probably not. 2nd class is 2+2 seating, 1st class is 2+1, with proportionally more legroom. First class does not have more luggage space, but it does have less people using the same space.
When you buy your tickets, a reserved seat will either be included or one can be reserved for a small additional amount. Not finding a seat is unlikely.
See here for more info: https://www.seat61.com/Europe-train-travel.htm#First%20or%20second%20class%20..?

Using OBB I have twice taken the train from Vienna to Budapest with my luggage; first time in 2014 I went second class and there was no problem placing my suitcase in the rack in the middle of the car, tote bag went in the overhead rack. The second time (last year) I was just barely recovered from major abdominal surgery and as a solo traveler was a bit anxious about dealing with my luggage and decided to go 1st class. It felt less rushed and easier as there were less people in 1st--I had a seat in a compartment for 6 with just 2 others for the whole trip, and easily managed to place my suitcase in the overhead rack--I prefer to have it near me, not out of sight. Access to the lounge at Vienna's hauptbahnhof was nice, too.

You can reserve seats in 2nd class, so if I were to go again I'd probably choose 2nd if the cost was significantly cheaper.

Buying your tickets well in advance gives you considerable discount. Depending on weekday and hour the almost 6-hour trip from Prague to Salzburg can be as cheap as EUR 24 (the other legs are even cheaper). Those are so-called »Sparschiene« (Saver tickets): non-refundable tickets only valid for that specific train (day and hour).
First class is totally unnecessary to be sure of a seat or a place for your luggage. For a few euros you can get a seat reservation and the overhead racks have plenty of room.
The above-mentioned Man in Seat 61 gives good information on your connections. Tickets can be bought at the trustworthy Trainline.

You said you will fly home from Munich, but at which airport you will arrive? Is your flight schedule fixed already? Without this information it is difficult to plan an itinerary with minimum travel time between the different locations.

The problem is that there is neither a direct flight nor a good train connection between Prague and Salzburg, whereas there are very cheap flights from Budapest to Prague ($40 lowest fare [I guess luggage will be extra]), but not good train connections.

Ideally you would arrive in Budapest, fly to Prague, go by train to Vienna, then by train to Salzburg, and finally by train to Munich.

We arrive in BudaPest and expected to train to Vienna then to Prague then to Salzburg and. Finally to Munich for departure.
I looked online and saw trains from Prague to Salzburg that took approximately 6 hours. Is this an error? I’m finding difficulty in the details and greatly appreciate any assistance.

Prague to Salzburg is indeed some 6 hours. It is close to 400 kilometers. On the train I can't find it a problem. Good for some reading, looking at the landscape rolling by, a little bit of day dreaming.

"I’m finding difficulty in the details and greatly appreciate any assistance."

The easiest way to get train schedules for almost all of Europe is to use the Bahn (German rail) website http://reiseauskunft.bahn.de/bin/query.exe/en, following Rick's tutorial: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules

Note that this only has prices (and bookable tickets) for trains that start or end in Germany. For other prices, here's a great list (from The Man In Seat 61) of where to book tickets: http://www.seat61.com/Europe-train-tickets.htm

One thing to consider about first class seating , Always check the pricing , before you purchase . It has been my experience that very often , first class is not very much more costly than second class . There have been many times when a first class seat might only be a few euro more , Obviously , if it is a substantial difference , second class is fine ..

There are rail pass options you can consider, all available from our rail travel pages about those specific countries. Seat reservations are not required for passholders on your route. I would not particularly bother with 1st class.

The cheapest pass is the European East Pass at $249 per person in 2nd class (or $362 in 1st class) for 5 travel days in Austria, Hungary, Czechia, and Slovakia, but not Germany. That covers 3 trips on your list. Would you have a use for the extra 2 travel days? Salzburg-Munich tickets are pretty cheap to buy locally, even on short notice.

The cheapest pass that would include Germany is currently the deeply discounted Eurail Global pass at $345 per person in 2nd class for 5 travel days in 28 countries. For sale before June 3, nonrefundable, and definitely overkill for this trip.

Some price examples:
Prague to Vienna, 2 Business Class (2 seats in a 4-person compartment) on Regiojet train, 44 EUR
Vienna to Salzburg, 2 Westbahn Plus seats, 120.50 EUR
Salzburg to Munich airport, 1st class Bayern Ticket for 2, 56 EUR

All of these bought spur of the moment.

The difference in price between second and first class. We can generally say that first class cost 50% more than second one.

Come to think of it, I don't believe they have 1st class on the Meridian trains from Salzburg to Munich. I know they don't on the S-Bahn to the airport. Then it is 31 EUR 2nd class.

Vienna to Salzburg, 2 Westbahn Plus seats, 120.50 EUR

That is completely overpriced. RailJet Sparschiene-Ticket is €19 each.

"It has been my experience that very often , first class is not very much more costly than second class . There have been many times when a first class seat might only be a few euro more"

"The difference in price between second and first class. We can generally say that first class cost 50% more than second one."

If you're wondering about these two seemingly contradictory statements, it's because they're both right. Bought in advance as non-refundable and non-exchangeable tickets, Steven's point is important - you can often get first class for only a bit extra. If that's the kind of ticket you want, it's always worth looking at the price of both classes before buying. Bought at the last minute as full price, fully exchangeable and refundable tickets, Ilja is right - first class costs about 50% more than second class. At that point, unless someone else is paying, second class is fine for most people.

Agree its a bit over priced, but show-up-and-go price for Railjet 1st class is 180 EUR for 2.
Gotta compare the apples with the apples.

I just purchased a second-class round-trip ticket to Vienna from Budapest for next Wednesday on the MAV (Hungarian railway) site and it cost $37 US.

Come to think of it, I don't believe they have 1st class on the Meridian trains from Salzburg to Munich.

They do but it's not worth it. The difference to 2nd class is minimal and there are only 8 seats per unit (so, normally 16 seats on a Munich - Salzburg train).

European East Pass at $249
Why a rail pass if you can have your trips for half the price with advance buying your tickets? The potential advantage of a rail pass is its flexibility. You don't need that flexibility: you will undoubtedly make hotel reservations, and so will know your travelling dates.

Excellent point Tom!