Personally I would NOT increase the needle size because a sock is more durable when knit tighter. It's also more comfortable knit tighter. A sock that is knit too loose makes it feel like you're walking on pebbles.
I haven't made a lot of socks yet, but I've learned a few things. If you are just making a basic sock increasing a few stitches should be fine.
If you are doing ribbing just make sure that you increase accordingly so the pattern remains the same (like add 4 stitches if you are doing 2x2 ribbing).
If the sock is tight across the instep you can make the heel flap longer and p/u more stitches. Then decrease down to your original number or you can leave more on the needles for a wider foot. On my last socks I made the flap longer and it made a huge difference for my high instep.
If you need a pattern this pattern gives instructions for casting on up to 80 stitches.
And a good book for socks is Sensational Knitted Socks
. It gives you lots of choices in size and gives help for adjusting for a perfect fit.