Margaret
If you are setting out using a lathe an offhand bench grinder is more ore less mandatory unless you constantly want to buy ready made tooling.
Lot's to choose from but heres one from Axminster Tools as an example – it would not take the cost of many inserts to pay for one
A noisy geared Black and Decker 5" version was the first accessory I bought with my first lathe. It was soon replaced with a small, much less noisy, 'Slibette 5" that I still use virtually on a daily basis.
Enjoy your adventure with machining wherever it takes you – it's a great pastime