I bought a Jackson Dinky DK2M a good while back, when I really wanted to play metal and not much else. Anyway, since then (about 3 years now) my style, especially when improvising/wiritng is now much more bluesy, kind of Hendrix/SRV/Clapton.

This made me think about getting a new strat, but due to budget constraints, I wouldn't be able to buy a decent one, but I do have an old Squier strat, which has a few internal problems I think. I'm pretty good with my guitar setups, so I've got it playing really well, almost as good as the Jackson, at least thats what I feel anyway :p

Problem 1, theres a lot of buzzing which occurs when I'm not touching anything on the guitar, this lead me to believe it's a grounding issue, possibly a loose wire. So I opened her up, but I still can't see any kind of problem, everythings soldered where it should be. and pretty well done.

Problem 2. The pickups, if I'm going to use this for all my blues stuff, it's going to need a sound improvement I think. What price range are we looking at to get a noticeable difference, also any recommendations?

Problem 3: It's a squier, and these have some flaws due to them being cheap. Since I'm not a complete guitar guru, is there anything I may need to change/modify if I was to use this guitar again?
Well im not an expert but i have a squier and i love it. i think with the buzzing u prob just need a neck adjustment if u go to a guitar center they did mine for 5$ and for pickup i would recomend just looking at a guitar center for some good quality fender pickups u might be able to find some for 50$ but i think most are around 100 or so. hope this helped
Problem 1: it may be the single coils but it's worth shielding the cavities. Get some copper shielding tape like this: http://www.stewmac.com/shop/Electronics,_pickups/Supplies:_Shielding/Conductive_Copper_Tape.html?actn=100101&xst=3&xsr=1056 and just stick it to the cavity and the underside of the scratchplate. Make sure there's at least a tab of the stuff connecting the two and make sure the layer under the scratchplate touches a pot. This will mean you can avoid soldering ground wires because the pots are always grounded.

Problem 2: I'd go the Fender Original '57/'62 Set. But this is best reserved for the pickup thread.

Problem 3: It's worth replacing the pots. Go for some alpha or CTS pots as they're the best quality. Also take it to a guitar tech and having them level the frets and set the action properly. It's probably good to replace the nut too. Go for either a graphtec or bone nut IMO.
Problem 1: Check out what matt154 posted above. Even after sheilding, you're probably going to have a bit of buzz from the cheap single coils.

Problem 2: We like Duncans and Fralins. Some of Fender's sets are really nice too. Check out some single coil-sized humbuckers (SD rails or little 59s) as well, you might like a fat strat setup for what you're doing. For decent budget pickups, maybe try guitar fetish/gfs. That way you can do A LOT of experimenting for a little $$.

Problem 3: Bone nut, setup and fret level, new tuners, might need a new jack if it's like any squier I've come accross.
Since you're in the uk i'd suggest looking at Iron Gear pickups. I've used them in all my builds and they're honestly better than pickups you can spend hundreds on.
So I had a go at opening her up to do the shielding, as was mentioned. Theres actually a large bit of foil (appears to be aluminium) on the scratchplate itself, but none on the cavity, so I've added some copper shielding. I'm still getting the horrendous buzzing, except when either at the 2nd pickup position (neck and middle pickup), or when the second tone knob is set to zero, which appears to cut out the sound (this only works on certain settings too). I'm guessing this is a problem to do with the knob, so will be replacing them early next week, and the pickups, to be changed at a later date. Any other suggestions what it could be?
It may just be the single coil itself. Does the tone or intensity of the buzzing change as you move around the room? if so it's probably just the single coil picking up stuff like flourescent lights or radio waves. Nothing you can do about that than pull them out and get some noiseless ones.