Second top-loading bobbins - those front-loading ones will do her head in if she's not used to them (she might be but I couldn't get on with them).
I have an electronic machine with more stitches than I use but the handy ones that the old '70s Singer didn't have are stretch zig zag (great for reattaching elastic to underwear, say), stretch straight stitch (good for taking up sweat pants), blind hem (good for hemming curtains - subject to the fabric tolerating it); incremental needle position (good for getting close to the edge when piping, especially when used with an adjustable zipper foot).
Will she be using the machine to take up hems on trousers with flat felled seams (eg, jeans), if so, does the machine have enough heft to get through up to nine layers (count 'em) of denim? Machines around the £100 mark will have nylon chassis that will flex when they encounter challenges like that - my SiL had one that DB bought sight unseen and it didn't last long!
That brings me onto the next point, which is weight. Sturdy machines have metal chassis but they bring another problem - if your mum is getting on in years she may struggle to lift a machine, particulary if she's showing signs of spinal degeneration (don't ask me how I know
) so it might not get much use unless it can be left set up on the work table permanently.
I'd recommend you test-drive some machines and take, eg, multiple layers of denim or canvas to see how the machine copes. Take some medium-weight fabric and test blind hemming. Check how heavy they are compared to your mum's current machine. Check how well it does a straight stitch - you would be amazed how poor some modern machines are at this compared with machines of half a century ago.