Barbarous radiates are fun, but I agree they can never be "collected" in the sense that other coins can, simply because 99% of them are unique one-offs, and many are simply too degenerate to even tell what they're supposed to be.
Personally, I accumulate all the ones I come across in lots, although I don't specifically seek them out unless they are something truly special. Some of my favorite examples of something "truly special":
- Types with a unique reverse - I'd love to see the celtic horse reverses Ben is referring to! CNG sold a lot with unique reverse types several years ago, long before I even collected ancients:https://www.cNGCoins.com/Coin.aspx?CoinID=94518
- Types that are in exceptionally good style, possibly by a former mint worker
- Types that aren't just Tetricus I/II, Divo Claudio, or common 4th century type (VLPP, FTR etc)
- Types that are extraordinarily small or degenerate
Some of my favorites that I've picked up over the years:
I theorize this one might be a stab at a Gallienus Zoo type?
A decent attempt at a Gallienus, with an indecipherable reverse
A mostly literate Victorinus with a portrait that looks nothing like him / Salus, but there's no snake and she's about to do a Kamehameha. And all the S's are huge and sideways!
A really nice and fully literate Tetricus II - I'm not even 100% sure this is barbarous?
A very rare coin of Tetricus II as Augustus - These are rare as barbarous coins, and a few (as in fewer than 10) examples are known that might be official - It's not entirely clear whether Tetricus II was ever made Augustus
Tetricus I with Apollo reverse - not a type normally seen
Also Tetricus I, but with the Tetricus II Priestly Implements reverse (This one is from @Ben)
Some fun highly degenerate types
4th century types
Constantine? Two captives with standards
An assortment of fun tiny (6-10mm) Fallen Horseman types also from @Ben
One not so tiny
Some barbarous AE4 cross types (I used to collect these too, but recently thinned out the herd to just the best/favorites)
And my most recent acquisition, a Celtic(?) copy of a first century Roman As or Dupondius; not enough detail to identify the original, but I suspect it's Claudius.