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Starting with a single family is what a lot of people do with diptera I think. I would guess the most popular is Syrphidae.

Asilidae have the advantage that there is good accessible literature on the family that a serious newbie could use without frustrating themselves too much (I mean here of course Stubbs and Drake, British Soldierflies and their Allies). The family is rated as easy to moderate with some species a little more difficult.

The disadvantage is that we are a bit light on with Asilid experts on diptera.info.

How often do you see Asilids? Do you have someone local who can confirm your IDs while you learn? I don't see enough in east London/Thames estuary to ensure I get to grips with them, but if you've got a handy heath, things might be different.