Fly into Zagreb - Split - Mostar - Dubrovnik - Budva - fly out of Podgorcia
Croatia, BiH and Montenegro are great places to visit, however a bit puzzling seems to be the choice of some destinations. In Dalmatia for instance Split is probably not even in top 10 most interesting places to visit. Yes, it is a big city (at least in Croatian context), but, imho, choosing it as destination to spend few days...khm... maybe just make it a base camp with "radial" journeys to more interesting places - Trogir, islands etc. Also slightly awkward seems the choice of Budva in Montenegro, especially taking into consideration that between Dubrovnik and Budva there is such a pearl as Kotor.
Seems there is a good train and bus between Zagreb and Split.
Yep, during the high-season there are usually a couple of daytime trains (roughly 6 hour journey) and two overnight ones. And obviously plenty of buses, however if you do decide to use the bus, then we would advise you spend some extra time and take one of the "longer" buses that travel by the seaside road (via Zadar, Sibenik) and not the highway.
And see there is a bus service to Mostar from Split and Dubrovnik.
There are buses between these destinations, although obviously not as frequent as domestic connections in Croatia (e.g. between Split and Mostar about half a dozen departures, a 3-4 between Mostar and Dubrovnik)
I assume there is no train service between Dubrovnik and Budva though and the best is to just take the bus to Budva and then I see a lot of buses from Budva on (www.busterminal.me/) to Podgorcia?
Long long time ago Dubrovnik had a railway line connecting it to the rest of the world, but nowadays it's only about buses. In Montenegro on the line Herceg Novi-Kotor-Budva-Cetinje-Podgorica buses run like every 20-30 min, so it's very easy to travel to Podgorica, even no need to think about tickets in advance or timetable - just get to the bus station and board a bus.
With this option do you think with bus/train this route would be doable? How are the services between Zagreb and Sarajevo? I would think there would be a lot of buses or trains from Sarajevo to Mostar?
There is daytime direct train from Zagreb to Sarajevo + multiple buses. Between Sarajevo and Mostar there aren't many train as one would predict - only two daytime train + again multiple buses, but in this case would really recommend taking a train - great scenery.
Trying to figure out if this options would give me a few days in each place and be able to get back to Zagreb without feeling too rushed?
Well, all the listed destinations aren't that big, for almost all of them a day or two is totally enough, imho. Thus two weeks seems to be more than enough time, even if you chose to travel during the day (NB: with Zagreb-Split and Zagreb-Sarajevo distance allows an overnight journey)