First of all, happy belated birthday. Second, welcome to Austin!
You should have no trouble finding a single bedroom apartment in the 700 sq ft range for $700 - $800 anywhere in Austin as long as you stay away from the numbered streets and outside of downtown. Our apartment is 630 sq ft and we are paying around $1000 a month, rent and utilities combined. We live near Parmer & Anderson Mill, which is in Northwest Austin, almost in Cedar Park.
The major tech companies are clustered around the Duval and Mopac (aka Loop 1) intersection. Lots of singles and d.i.n.k.s. in that area. Things seem to be slowly centering around the "Domain", a large shopping and apartment living complex (actually it's more of a neighborhood now). IBM, National Instruments, and maybe even Samsung are roughly within walking distance. This area would also put you relatively close to the job sites you mentioned, but far enough away from the mess that is I35.
Traffic can be pretty rough everywhere in Austin so you may want to consider living close to where you will work. I wouldn't recommend commuting from one side of the city to the other. I work with a few South Austin residents and they claim hour+ commute times to and from our office in North Austin.
Once you figure out where you are going to move, contact an apartment locator. Austin has had an absurd influx of people over the last 5 or 6 years. Housing development (like roads and infrastructure) has fallen behind and the renters' market has been awkwardly picking up the slack. Finding vacancy may be difficult without an agent.
