Most conventional baskets can take about a 5 gram range of dosages: 7-12 for singles, and 13 to 18 for doubles. The lower the dose, the finer the grind you need to get the correct flow. Low dose/fine grind shots are highly extracted and mild; high dose/coarse grind shots have lower extractions and more powerful flavors.

The new wave of baskets made by VST, also labelled LM Strada, are different. They come in 15, 18, and 21 gram sizes and the dosage needs to be exact. They all take fairly fine grinds, with the 15 taking the finest, the 21 the least fine. These are a good choice for lighter roasted, "3rd wave" coffees, since these require fine grinds, but tend to be extremely finicky if used at low doses in conventional baskets (I guess they don't work in a thin puck; but I'm not sure why).

mathof wrote: ... coarser ground shots ... have lower extractions (less total surface area exposed to brew water) ... what makes them have more powerful flavours?

It's a little counterintuitive: The smaller molecules dissolve/extract more quickly than the larger molecules. On the whole, smaller molecules have more intense flavors; while larger molecules, especially chains, add to mouth feel and buffer the flavor.

This means that the measure of solids extraction from the puck also is an indication of the ratio of flavenoids to buffers. As a consequence, a highly extracted shot with a low brew ratio is going to taste a lot softer than a low extraction shot with a high brew ratio, despite both having the identical TDS, i.e.the same level of coffee solubles, in the cup

The VST baskets are useful for beginners, since they force you to weigh the dose and use correct grind settings. They are also good for people who want very precisely repeated shots. If you have a modicum of confidence in your own taste, and are OK with a modicum of shot to shot variance, they are a waste of money.

People often go into a buying frenzy if they cannot get a shot they like from a coffee that others have praised to the sky. But there is a huge difference between pulling a good shot you happen to dislike and pulling a lousy shot. Until you can tell the difference; you will be spending a lot of unnecessary money.

I got an 8 gram and an 14 gram basket with my espresso machine, and was wondering to what extent you can vary in the dose for these baskets. I got to the habit of overfilling both baskets with 2 grams, but I am not sure to what extent less (or more) space between the shower and bed plays a role in shot quality.

It is not so much the amount of space between the shower and the puck, just that you do need to leave some space. The opt-cited way to test is to put a nickle on the puck, put it in the group head and then remove. The nickel should not have depressed all the way down into the puck.
As for for taste, the more coffee the bolder the taste, all other things considered equal. Somewhere on this site, you should find a nice little diagram showing the effects of increasing/decreasing dose and increasing/decreasing grind size.

Also, does the fluffy-ness of the grind matter, or is this all tamped away?

That's a tough one. Some people say yes. My simple palate cannot pick up the difference. I think it is much more important not to have voids in the puck, or channels down the sides. So, a fluffy grind should pack better, I guess. But, if you tamp with the typical 30# pressure used by most in North America, I think you're right...all that fluff gets packed down. Personally, I don't pack that hard, but I do rock the tamper a few times in different directions before the final tamp, to be sure there are no voids.