Any small lathe will do that fine. For small projects like these you wont have large out of balance stock to rough so variable speed isn’t really a must have.
Depending on budget, I’d look for a bench top lathe with as many extras as poss. Items such as a selection of quality turning tools, a chuck, drive centre, live centre, etc are often bundled and a package in used condition can be a bargain.
Many will extol the virtues of the older design twin bed bar record power machines (not a fan myself but no matter), there are many similar type bench lathe - look in the cheaper end of the axminster range, and probably at the other end of the price point is something like the Vicmarc 100 type lathe.
One thing to consider, if you get a spindle thread of ideally 1”x8tpi or pref M33 x 3.5 then if you decide to trade up to do bigger projects in the future most of the accessories you have will be still suitable.
Simon