You are going to have a challenge overwintering that hive if they have been queenless for 8 weeks. The numbers of bees are going to be dropping fast now if there is no brood, and the nurse bees will have matured into foragers, making it hard for them to care for eggs and larvae. Any way you could merge them with another hive? Failing that, would anyone at your bee club be willing to donate a frame of bees, eggs and brood to your hive, or at least a frame of capped brood? If you are going to try with a purchased queen, you are going to need newly-emerged bees from such a donation, to care for her eggs.
To answer your question about what type of queen, you need to decide what characteristics you want in your bees. Ed @Red_Hot_Chilipepper makes a good point, a local “mutt” queen is likely to be healthy and well-adapted to your local climate. However, most of the mutts I had in the UK were not the nicest temperament. Here is a useful chart of the various characteristics of different types of queen:
I like Italians, or Italian/Cordovan crosses, especially if they have the VSH trait to help with varroa management. However, they eat a huge amount over winter, and you are very likely to need to feed them regularly. Many people in the UK like Buckfasts, if you can get them. However, if they replace the queen, the F2 generation daughter queens can be very mean. Carniolans also do well in the British climate, but they have a tendency to swarm early and often. Perhaps @Dee will chime in with her thoughts too. She is a long way west of you, but she has quite a bit of experience with which bees are readily available and where to get them.