Honestly, I would really suggest going for private lessons at first, especially if ur just learning to jump you want the trainer to be able to focus just on you at first, making sure you are doing everything right and you are being as safe as possible. Group lessons are good once you have the basics down. When you are confident enough to ride with others, you can really learn a lot just by watching other people ride. If you are just taking lessons once a week, ask your trainer if you can take private lessons until you have the basics of jumping down and then you can switch to group lessons....just my opinion, though :)
You should be spending a while on the flat which may include riding on the rail and over cavaletti. You'll learn about posting to the trot, strides between fences and lots of other things that'll build up to jumping. There are a lot of different english classes and i'm not sure of the names of all them but yes, ther are classes just on the flat, just jumping, and a combination of both.
Sorry if i'm making you sound like a beginner not sure what you know already...lol
Hope I helped!