You can still find so called stacking systems as cheap (and probably dodgy) imports from the far east with brands you will have never heard of for under 400 an Amazon/Ebay but personally I would touch them with a barge pole.
For some decent and likely to function for more then five minutes and/or not sound awful, probably best off looking over bundles of receivers + speakers and/or mini systems from the like of Peter Tyson and others if after new, but you will likely have to stretch well over 400 for a complete new system by the time you add a turntable.
About the only combo of a mini system + TT that in this kind of price range (still quite a bit more by the time you add a TT) is probably Denon D‑M41DAB mini hifi system (CD, FM, DAB and an input I think). Add another 120-150 for a turntable from Audio Technica, Denon etc with a built in phono pre-amp. There may be similar mini systems from Yamaha, Marantz and others, but will still be same problem - need a separate turntable.
There are some all-in-ones with a turntable instead of CD (Project Juke box or whatever it is called), so then opposite problem applies and need to find a separate CD player. I would expect convenience of CD player on the same remote and a separate TT would be more convenient to use than all in one with a TT and a separate CD player.