the screw has to take the weight into the brickwork. Plaster has almost no strength.
In my house the plaster/render is about 18mm thick, so the first 18mm of the screw and plug length are no use, plus whatever length of screw is inside the article I am fixing. So I mostly use 50mm screws. the hole must be deep enough that the screw will not reach the bottom
If you have an old house, the plaster may be very thick or the bricks very soft.
Personally I use brown plugs, which are plenty big enough for most jobs, but opinions differ. I have not got one in my hand but they are about 35mm long. I drive them below the surface of the plaster slightly (this reduces risk of plaster cracking) by putting a screw into the hole and tapping it lightly with a smallish hammer. You can then withdraw the screw by loosening it with a screwdriver and the plug should be tight in place.
If you use an excessively small drill in a good firm brick, it may be impossible to drive a screw into the plug as it will be too tight.
A couple of 50mm x 4mm screws, into tight-fitting brown plugs, will hold a wall cabinet full of kitchen stuff, which is pretty heavy. For something light, like a picture or a wall clock, you could use smaller.
The screws and plugs you get free with "things" are usually too small.
Depending on how crumbly your walls are, the drill that (according to the sample on the wallplug strip) ought to fit, might make a loose hole. If you have a set of masonry drills, try the next smaller size and make a note of the size that fits, for the future. Clear the hole of dust (which has no strength) after drilling, either with the vac cleaner snout, or blowing, or by squirting into it with your houseplant mister (this makes dirty water run down the wall though)
However: A tip I found on here which is amazingly helpful if you have crumbly walls and loose plugs:
Drill and clean the hole
Put in the plug and discover that it is loose.
Take a tube of "NoMoreNails" or similar with a long nozzle on it.
Push the nozzle deep into the hole and squeeze as you withdraw it, so the hole is filled from the bottom and does not have a bubble of air at the end
You now have a hole of suitable depth, filled with NoMoreNails.
Poke your plastic wallplug into the hole, so that the outer end is slightly below the surface of the plaster, and wipe off the excess with a damp sponge (with practice, you will learn to stop squeezing before you fully withdraw the nozzle, so that you waste less) the plug is now completely encased in NoMoreNails and there is no air gap.
(You may find it easier to push the plug in if you insert a screw into the plug and give it a turn or two, then you can use the screw as a handle and it prevents you losing the hole in the plug under excess NoMoreNails
If the plug was really loose, leave it overnight to harden. If it was a good enough fit not to spin in the hole, you can now fix your bracket or whatever and drive in the screw without leaving it to set. If the plug starts to turn, stop screwing and leave it overnight to set.
The tip was posted by gazza2 on this site not long ago. I have seen professional injection kits using resins that are more expensive
I have been DIYing since long before you were born, and have only recently heard this successful this way of dealing with loose wallplugs. I know no other way that works as well.
