For both games, as above, a good stance is key to a good smooth cue action. Rest your chin very lightly on the cue and make sure it doesn't come off it until you have struck the white ball and followed through. Again, as above NO jabbing actions, only smooth cue action with good follow through.
For snooker, spend a lot of time working around the reds, black, pink and blue and also with just the colours (yellow-black) on their spots. Try not to spend as much time practising long pots, as the most important ones will be fairly short shots when you're in the balls.
The only long shots I would really be spending any time practising in snooker is safety shots - try to practise getting the ball back into the baulk end of the table from various angles, and getting it to rest as close to the cushion as possible. The whole idea in snooker is to pressure your opponent into making an error and giving you a chance.
For potting and positional practise I would normally set up a half dozen or more reds in their normal position, with a couple free to pot. Practise potting these and think about where you want the white to finish to make your next shot as easy as possible. Try to always leave the cue ball far enough off the cushion that you can rest your hand flat on the table - this makes a big difference with the level of control you will have.
Really make the effort to keep it as simple as possible - watch the best of the pros out there, they keep it simple, only using lot's of cue action when it's the only option left for them. A little bit of side / top / screw etc is great, but keep it to a minimum.
When it comes to pool, it is very similar in a lot of ways. Again, simplicity is the key - watch the best players, it looks so simple!
I would assume you play 8-ball? Practise your break! I can't stress this enough, but a good break off shot can more often that not win you the game. Don't just thump them from straight on, move the white out towards the sides of the table, add top spin, maybe a little side spin too. See what works best for you. If you can have a good consistent break off shot in pool, then more often than not you'll win the games where you have the break.
Otherwise what I would practise in pool is position and angles. It is really important that you know all your basic angles in pool and can get to your next ball from almost anywhere. If you can't get to your next pot, then work out where best on the table to leave the ball so that your opponent doesn't have an easy shot.
Generally in pool if you can't pot, try to leave it safe as possible, with the cue ball tight to a cushion, and try to keep your object balls off the cushions. It's always easier to pot them and get position on the next one if they're not tight to a cushion.
And as for cues, yeah you can pay £3-500 for one, but will it make you a better player? Not likely to be perfectly honest. I played for years with a cue that cost me £75. The key here is get something that you are comfortable with. Cues are all wighted differently and what suits me would likely not suit you, so get out there and try a few if you can. If you plan on using the same cue for both, then I would suggest you go with a tip size no smaller than 10mm, maybe even 11mm as you will put a lot of strain on it when breaking in pool.
What I would suggest though is that if you buy a cheap cue, get it re-tipped with a good quality tip. I always used Elkmaster tips, and spent a lot of time shaping them to a nice smooth dome. Oh and one last thing - PLEASE use GREEN chalk!!! I see so many people using blue chalk and it drives me nuts, it leaves the cue ball and cloth in such a mess!!!
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