I would probably stick with smooth foods and purees without any lumps in at all *and at the same time* finger foods which he can pick up himself and self feed.
The thing with having lumps in puree is that some LOs are not expecting it and so they suddenly find a lump in their mouth and not really sure what to do with it, try to swallow and gag. The finger foods that he self feeds, he knows they are different to the purees so whilst it might still cause some gagging he does know if he picks up a piece of finger food and puts it in his mouth that he is going to get a solid bit and he will gradually learn what to do with it.
Spitting out is fine, gagging although doesn't look nice is not really harmful, choking though is the thing to watch for. It sounds like (as HH said) he still has a very active gag reflex, the gag reflex is further forward in babies which helps to protect the airway.
Another thing LOs can do is swallow a piece which is too big, so it's gone past the airway (not a choke) and then their body expels it because it is too large - this is like a vomit although with some just the big lump is expelled whilst with others they will also expel the entire contents of their stomach. Again it is a natural way for the body to protect itself but can be a bit distressing, often more so for parents than for the LO - I can remember mine doing this vomming up large lumps onto his high chair tray and then picking it up and having another go.
As HH said you can try different textures with the finger foods, sometimes drier foods are easier rather than the softer pulpier foods (eg I worried more about soft bread balling in the roof of the mouth and DS being unable to dislodge it than I was about a toasted crust which was hard and less doughy). You might also try some different pasta shapes for example which, he might find easier to swallow than mushy banana (you can just serve cooked without any sauce, easier for little hands to pick up and manipulate, sauce can be served separately).
If you are able to find a paediatric first aid course in your area you might find this helpful, they go through what to do if LO chokes. Just knowing what to do can help to reduce the worry of meal times.