First check what your friends and relations have kicking around in their attics. If you get lucky, get it serviced before you plug it in. £100 on fixing a vintage bernina, elna or Viking will leave you with a much better machine than £100 on something new.
But new machines are fun too. I'd probably choose elna or janome for a budget machine, but if you've got a proper sewing machine shop within reach, get in there and try them out (decide what you can afford first, or you'll be seduced by 1001 decorative stitches, which you'll never actually use)
Features you NEED: straight stitch, zigzag, some sort of buttonhole function, interchangeable presser feet, bobbin winder, light, reverse stitch
Nice to have: free arm, dedicated overlooking stitch and foot, up/down feed dogs, one step buttonhole
Fun, but frivolous: all other stitches, automatic needle threader, auto needle up/down.