Saw that you're already considering the Prusa Mk4, and that was pretty much what I would have recommended for your price range. Prusa machines are not cheap, but once assembled they just work. But since Prusa has an open ecosystem and open-sourced pretty much everything, you have complete control and choice on what software you want to use to accompany it, and you also can mod the printer to your liking if needed.
The Bambulabs printers some others mentioned are different in that they are a closed ecosystem. You get the printer as-is with very little playroom for modifications and the software side (slicer) is AFAIK also pretty locked down to what they ship with the printer.
For the slicer, as mentioned it depends on the printer. If you go with Prusa, pretty much any slicer will work. To name a few, PrusaSlicer, SuperSlicer, Cura...
If you go with Bambulabs, (AFAIK) you're restricted to using their slicer.
For designing your own models, there's also a plethora of programs available you can use for free. Be it CAD programs like Fusion 360, SolidEdge, OpenSCAD, FreeCAD, modelling software like Blender, or many many more.