My 23 year old son is planning a backpacking trip from Italy to Hungary to Germany returning to Rome. Would a bus pass or a train pad be advised?
Not really. Trains with tickets bought early are probably the best and cheapest travel for him. 2 1/2 months is a long time to be traveling from place to place. And it's really hard to plan very far ahead when you're 23 years old because you never can anticipate the detours and the people you're going to meet along the way. Budapest, Vienna, Prague and Munich are priority cities for young Bohemians.
Nope. He would be probably be confused about what trains he could take or end up hoping on a train not covered. This forum every week see a lot of confused people considering rail passes or that bought rail passes confused because of not reading the rules on how they work.
Trains in Italy are fairly inexpensive even for walk-up tickets. The same is true in Hungary. Some trips in both countries are likely to involve buses (not covered by a rail pass). In Germany, there are bargain-priced regional day-passes for trains on weekends and after the morning rush period on weekdays that can be an excellent deal, so many rail trips can be surprising inexpensive--even more so if your son meets another traveler and they decide to travel together to the next city.
Therefore, it's highly unlikely that a rail pass will save your son money on this trip, but it's impossible to say that with 100% certainty without knowing exactly what his itinerary looks like--which probably even he doesn't know at this point.
Note that doing this trip without flights will require crossing Austria at least once and may also mean transiting Slovenia and/or Switzerland. Of those three countries not mentioned in your post, Switzerland has by far the most expensive trains (and hotels and restaurants). Avoiding Switzerland will save money, but there's incredible scenery there. If your son decides to spend any appreciable time in Switzerland, he might benefit from some sort of Swiss pass or half-fare card.
Early purchase of a few long-haul train tickets (if the itinerary has such travel legs) could save quite a bit of money, but those tickets will probably be non-refundable/non-changeable, so that technique is viable only if the those travel dates can be pinned down. For example, if your son wants to put his Italian stops at the end of the trip, he might know that he wants to travel from Rome to a fairly distant point either late on his arrival day (allowing for flight delays) or early on Day 2. That's a ticket that might be bought well in advance at a discount price.
If he instead decides to see Italy at the beginning of the trip (it will be the warmest destination, so this would be smart if the trip begins early in the year) and plans to end up in Hungary, traveling straight back to Rome, that final long travel leg would be best done by air. That airline ticket will be cheapest if bought well in advance.
For an international trip like this, trainline.com is perhaps the easiest place to check long-haul fares. Domestic fares within each country can be found on the appropriate train company websites, which will also be the cheapest place to buy tickets in advance. Seat61.com is a very good source of train information for all the countries in Europe and mentions a cheap way to travel to or from Germany and include the highly scenic Bernina Express in Switzerland; scroll about halfway down the webpage I've linked to.
For simply checking rail schedules during the itinerary-building process, I find the Deutsche Bahn website by far the easiest to use, but it doesn't generally provide fares for trips that neither begin nor end in Germany.
Buses are often cheaper than trains, though they are frequently slower when both forms of transportation are available. For a quick check on what type(s) of transportation are likely to be offered between any two cities, the website Rome2Rio.com can be helpful. However, it's important to clearly understand its limitations: The fares, travel times and frequencies displayed on the Rome2Rio website itself are very likely to be wildly inaccurate. Travelers need to drill down on Rome2Rio to find the names of the bus and rail company providing service; usually there's also a link to their websites, which is where one needs to go for accurate fare and schedule information.
If I already know there's no rail service or only inconvenient rail service and am just looking for bus information, I usually find it easier just to Google something like bus Florence to Siena.
There are various ways to save money on train tickets, primarily by booking early, taking slower trains, or traveling in somewhat cheaper countries, which he partly is doing. (Being a youth is rarely a discount category on train tickets.) But since 2.5 months of traveling is a long time, he might really pack in a lot, and those tickets all add up. The more he has planned, the better he can make a meaningful comparison.
When choosing between options on the Eurail Global Pass, a more "minimal" version could cover only his 10 ($310) or 15 ($382) longest travel days within a two-month window. Continuous passes for 2 months ($567) or 3 months ($699) provide many more days of coverage, which he may use or not, but with very few trains not eligible. These prices are based on his age, as well as the current sale that lasts through Dec. 30.
Additional seat reservation fees vary by country and type of train, further detailed our the relevant country pages. For his route, they're most relevant to/from/within Italy.