IF indeed aiming for Beograd-then mostly have to come back same way, with connections not that best. OR-of course, fly back from there at the end. As such that city does not really have very much to offer- even more if one compares it with other same-style former eastblock towns.
You get -it has been so often said, also on seat61- the very best in value using it in countries with good networks and frequent service-preferably even without all those cumbersome extra REServ. So thats Deutschland, Suisse/Svizzera and Österreich. CZech can be neatly put in between and by making a sidetrip into Danmark you get good value-as local fares are pretty high (which means good savings!).
IF you grow a little older-to senior status >65, ALL transport, basic, is free in ALL of HUngary. Ditto for urban networks in CZech. So that would also mean a pass is wasting precious money. But I guess thats for later-and who knows how it will be then.
Deutschland-mostly those sleek white ICE trains, are notorious for delays and nowadays even cancellation, though in the end one usually arrives.
Oh-end to smash perhaps some ideas: that 1st will bring nothing extra as wider seat and mostly a quieter civilised environment.
Thats why I once a few yrs ago grabbed a 1st cl and rode in your UK (then still without all the entry-fuss end even payments there is now for us poor EU-souls) on IC trains and got food on offer.
More ideas also on the forum of the passes: community.eurail.com , the very same Q comes up there quite a few times, and also mostly from out of the UK.