Secondhand machines reconditioned from a dealer/sewing shop will be a good point to start ... I have bought many off Fleabay ... but that generally involves travel ... Oh yes, My then husband travelled to all corners of the country for me!
.... but you do need to know what you are looking for.
If you asked 100 TSP members in 100 minutes what the best sewing machine is you''ll probably get 100 answers ... Everyone has their favourites!
Good brands are Janome (my favourite), Brother (not for me) but I would definitely avoid Singer ... unless its an old black metal model, which do come up and if you are mechanically minded can be restored and then sew Beautifully ... You'll find out more in the Vintage machine section of TSP .... but do avoid 'bargains' from Lidl or Hobbycraft etc ...
Do you have a SM shop nearish to you? That might be your best first stop, especially if they have more than one brand in stock, you can try a couple to see what suits her.
If no shops near you there are some very good Online shops, SMD is one ... but do make sure you avoid a certain one ... Is it Coopers, Ladies ??? (some one will tell you)
Im sure there will be more better informed replies than mine along in the wink of an eye ...