TBH, I think the OP's best bet is to go to a bicycle recycling place and get something from there. There's lists and recommendations in the "General Cycling Chat" section of the forum.
There'll be good bang-for-buck, and no one will try pushing something that's way out of budget. Likely you won't get anything fancy, but you'll end up with a decent bike that does the job.
And to the OP - frame sizing is only a *guide* as to what size bike you need. Everyone's anatomy is different, so don't always take the salesperson's word as to whether a bike will fit or not. Chances are they're only going by the chart they've been given rather than your particular measurements. As I mentioned upthread, the two basic tests you do in order to see if a bicycle fits is:
a) Stand over the thing. If you've a good inch clearance between the crown jewels and the top bar, the frame is in the right ball park (see what I did there?) and...
b) Put your funny bone against the nose of the saddle and your fingers on the headset (the bit that holds the top of the forks to the stem). If your middle finger reaches the middle of the headset, then the bike has the right reach for you.
If A and B both apply, then the bike will fit you.