Let's see...
-Razors; Schick Quattro & Intuition, Gillitte Venus. Have used all 3, found the Quattro works best, same as the Intuition, but w/o the soap
strip, costs less. Venus works better on my arms though.
-Depilatories; Nair, Veet. Strong Base or Alkali solutions, they will burn the skin. Best not to use if there are any skin cuts or irritations.
-Waxing; Good but messy, not to mention sticky! May cause bruising, especially on the inner thighs, painful,but last longer. If you are not
meticulous and good with your hands best to have done by a pro at a Salon ($$$).
-HRT; Those on HRT are reporting less problems and less hair growth.
-Laser; Permanent solution, is expensive, guesstimate avg $500.00 per session for both legs, 4-6 sessions avg = $2,000 -3,000.00!
I suspect you live in a more Northerly location, cold & dry, little sun on legs...may be getting shaving Folliculitis, possibly Eczema. Try not shaving or using Nair or anything for at least a month, then consider using one of the mentioned razors, a fragrance-free body wash or liquid baby soap, makes for a slicker shaving surface. I use Aveeno Fragrance-free Body Wash plus K-Y Jelly (generic will do), mix the 2 together and slather it on your "wet" legs! Turn the shower head to the side to avoid washing it off. Consider at least 2 shaves, first in the direction of hair growth, second against the direction or "grain"
Knees and ankles more prone to nicks, so keep a tube of Neosporin handy to dab on the cuts afterwards.
Pay attention the direction of hair growth, it can be different for each area of the leg, especially the Upper Leg/Thigh. It takes time and good technique, so please be patient, also moisturize your legs afterwards. You want to avoid clogging the pores. I found that Avon's Skin So Soft and Dove's line of Oil Body Wash's work for me, use to use Emu Oil mixed with Sweet Almond Oil, one of my cat's liked it and would lick it off of my legs! Talk about exfoliation

But it is expensive. Another previous suggestion is to exfoliate the legs 24hrs before shaving and no sooner than 24 hrs afterwards, in time this will no longer be needed as the shaving will do this.
In the end...find what works best for you! A lot of great input and items suggested so you should find something that works well for you!