In your shape and your condition, I would get a used mountain bike in good working condition and then put narrower street slicks on it. Something without suspension like Zippy's first bike.

Get something like this used Trek 800: http://orangecounty.craigslist.org/bik/2848468894.html

And then mount something like these Forte Metro-K tires: http://www.performancebike.com/bikes...8_20000_400238

You're looking at $120 for the bike and $30 for more road worthy tires. Save the rest of your money. Then a year later after you've ridden a bunch of miles and gotten into better condition, you can look around and find something that fits you really well.

[edit]The Trek referenced has a 19" frame, and at 6'3" you're going to need something quite a bit bigger than that. It was just an example[/edit]