$1200 for a wheel is outrageous unless it is a very, very limited edition wheel ... like a Golding ... which isn't antique.
I can pick up antique wheels for $100-$200, and only will if they are unusual.
If you want one to sit in the corner and admire, you can usually pick up a non-working wheel for well under $100.
As for the OP. I started with a drop spindle and eventually got my first spinning wheel.
How long it would take you on either apparatus depends on how much time you dedicate to the art.
For making a sock yarn, you'll need to spin very thin, then ply it.
The 'weight' of the yarn that you spin is all in how evenly and thinly you can draft your fibers.
The even-ness depends on how well your prepare your fiber for spinning.
I've found sock weight yarns easier (at first) to spin on a drop spindle. As I progressed in keeping my treadling & drafting even, I now make sock yarn more quickly on my wheel.
If you have a lot of time to dedicate to spinning in one place, the wheel is the way to go. If you are on the go a lot and perhaps get stuck in traffic, at red lights, waiting in lines, watching your children's whatever practice, the you can get more yarn completed on a drop spindle since it is so portable.
I'd suggest starting with a drop spindle. Check out Abby Franquemont's Drop Spindling Basic videos and even her book 'Respect the Spindle' published by Interweave Press.