My view, having run around Romania and Bulgaria last year, is that the best route really comes down to personal preferences about comfort and timings, which are different when you are older.
Seat61 gives good low-risk advice, though that means he now advises a night in Bucharest eastbound.
On the two bridges, although eastbound times are broadly similar it depends on connection risk and where you feel like staying a night. Scenery: (Ruse)Gorna Oriahovitsa-Stara Zagora is spectacular, climbs to 1000m with very little tunnel including a 360 degree tour of a hill top at 900m. (Vidin) through Dimovo then Mezdra-Sofia is beautiful too along an alpine-feel valley.
Working back from those:
Via Ruse the only train is 1011 (now, used to be later) from Bucharest so your choice of Budapest-Bucharest depends on whether you want to spend a night at Bucharest and/or sleeper from Budapest. IC79 arrive Bucharest 0936 so you could go on the same day but because reliability is awful (crap track speed restrictions and massive congestion) seat61 advises against it, but it calls at Videle at 0832 and the Ruse train leaves there at 1127 so that should work, but Videle station may not be where you want to spend a couple of hours although there is a small supermarket.
Via Vidin the only train is 0655 from Craiova. IC79 from Budapest stops at Craiova 0530 so that connects too. If not, stay on it to Videle or Bucharest, but you would need a reservation that far (so on Interrail reserve to Bucharest, if paying rebook as you go). Vidin-Sofia arrives 1730-ish (shuttle or tram from Sofia Sever), onwards to Turkey departs 1845 but I would not risk it.
So it comes down to how long you can endure on trains without a hotel, where you feel like lingering between trains, whether changing at 0530 at the equivalent of (much quieter) Crewe is OK or not, how much you like changing plans as you go or want to pre-plan. Oh, and the fun of getting reservations for Interrail (I was paying rather than using Interrail days)
For the Budapest-Bucharest routes there are recent threads on this forum. Both ways have pluses. The first 5h from Budapest is uninteresting. Or split it into daytime travel, I would stop at any of Arad, Timisoara, Drobeta-Turnu Severin, Alba Iulia, Sibiu, Sighisoara or Brasov for a night. Timisoara, Sibiu or Brasov probably the most interesting, personally Bucharest was underwhelming. Further on I'd choose Veliko Trnovo or Plovdiv though Sofia has hotels near the station and is fine.
Westbound: via Vidin lands you with hours in Craiova or overnight whichever way you carry on, so Bucharest probably best.
Final PS, because I haven't seen info on it elsewhere, for Arad-Bucharest overnight there is also Astra Transcarpatic (train builder running train services) whose sleepers look more recent than CFR's (some of which they built/rebuilt) and you can book luxe en-suite which is pot luck on CFR but were full on the nights I tried to book, but do not accept Interrail. Anyone used them?
