Hi there! Hope your house sale is going well. You are looking at some very different areas there, so would be useful to know what kind of things you like to do, or where you might be working if relevant?
Matlock is a lovely town, all the amenities you'd need, plus nice park, some lovely traditional houses, and closest to Peak District so some beautiful walks, places to visit etc. has train station with direct (but not fast!) links to Derby and Nottingham. The downside of Matlock is that traffic can be very busy in summer because of tourists on main road through Matlock up to Peak District.
I don't know chesterfield very well, town centre seems fine, big traditional market, good access to M1 and Sheffield, some lovely areas on outskirts.
Littleover is a suburb of Derby, so good bus links into the city and good train links from Derby to lots of places (direct trains to London and Scotland). There are some lovely parts of Littleover, some gorgeous traditional houses, then like most cities, some less nice parts. Derby has everything you need.
Ilkeston is probably where you'd get most for your money. It's a small town but has most stuff you'd need, lots of retail parks nearby including ikea. At risk of getting myself into trouble on here, it's not the most charming of places. Also worried that as you posted here a while ago you may have already found somewhere and if it's Ilkeston then ignore what I just said! Good bus links to Nottingham.
Hope that helps, happy to offer more help if I can!