You don't go into much detail of what you're brewing, how you're doing it, how quickly you're doing it etc. So here are my thoughts for what they're worth. The twang you refer to I tend to associate with the cheaper sort of kits, often referred to as 1 can kits. The twang is caused because you're using sugar in place of malt and it's much worse until the brew has matured for several weeks in the bottle. Don't believe the timings they give you with the kit - they're always way too optimistic. In my experience 1 can kits need a good 2 weeks in the fermenting bin before they've finished and cleared a bit. I know some people will leave it even longer. You then bottle. Some kits are drinkable after only a week, but I've had others that need more like a month til they're at their best.
Then there's the more expensive kits, often referred to as 2 can kits. I've only ever done 1 of these and it has no twang at all because all the fermentables are malt. Some people cheat with a 1 can kit and don't use sugar but replace it with extra malt - so basically converting a 1 can kit into a 2 can kit. Because it's all malt, fermentation can take a lot longer - maybe even a month in the FV - but you'll be rewarded by a brew that's as good as anything you'll buy.
A further step up are `all grain' brews, either brew in a bag, or done the `proper' way. I've only ever done 1 all grain brew and it turned out c**p - as all grain takes a degree of skill and knowledge you don't need for kit brewing.
You should also bear in mind what your water is like. Different kinds of beer are best with different kinds of water. For example we have very acid water here - which is very good for stout, okay for bitter, but bad for lager. I've tried brewing lager but it doesn't come out right, but the stout I make a lot of is excellent even though it's a 1 can kit.
The 2 can kits cost about 20 - 25 quid which may seem a lot but it's only about 60p a bottle if it's a 40pint kit. So 1 can kits can be a false economy as you're only saving about 10p. You can lose some of their twang as well, by making up to a smaller volume and using less sugar, but of course if you do that you're making it dearer/pint so you may as well have started with a 2 can kit in the first place.
A good bit of advice is always check out the beer kit reviews here on this forum before you buy a kit. Some - like the gluten free kit you mention - everyone says is awful, but others seem universally to be liked. Stick to those.