Guitar tech is one of my many professions, so here's my thoughts.
Does the hum only come on when you aren't playing? Does the hum go away in positions 2 and 4?
If that's the case, that's the nature of the beast. Single coil pickups hum, and are prone to electrical interference. You can relieve some of this with a different pickup that has better potting and sheilding, but that's not the only way. Some rooms just have a bad electrical environment (eg. fluorescent lights in the circuit) and pickups will hum louder there than other places. For example, I have a killer Tele that sound good in my house, but is extremely noisy at church because of the wiring in the building. In this case, the noise only comes on when I am not playing, so I use a noisegate with the proper threshold to take out the noise in between jams.
The question is, aside from the hum, do you like the tone from your pickups? If you like the sound, then you can figure out ways to reduce hum without swapping pickups. You can shield the guitar and that will reduce electrical interference. Here's an great article about doing that
http://www.guitarnuts.com/wiring/shielding/shield3.php . There's also the noise gate idea too.
Now, if you don't like the tone, there's plenty of humbucking pickup options that will fit in your strat. Each of these pickups have their own tone, so it's a matter of the type of tone you like. If you can give me some idea of the tone you like (hot, fat, vintage, sparkly, etc.), I could give you a recommendation. However, my ears hear a difference between the humbucking and non-humbucking single coils. In one instance, I actually put the humming, noisy single coils back in because I just liked the sound so much that I learned to live with the hum when not playing. I just got into the habit of rolling the volume down between songs.
