I think you can get a pretty decent bike and all the necessary components for $750. An entry level road-bike from a LBS can be had for around $600 easily. It will probably be an aluminum frame bike with a carbon fork, which is what I ride and I like it. It won't have the best components, but I doubt you will notice the difference as a beginner. Also, components can be upgraded later; as long as the frame is decent and worthy of upgrading. Then, a decent helmet is around $50, a decent mini-pump is around $20, tire levers are around $5, a multi-tool is around $20, a saddle bag is around $20, and spare tubes are around $5 a piece. Add a pair of biking shorts ($50), and water bottles and cages ($15) and you are good to go. Your total so far: ~$750-$800.
Lot of the items I mentioned can be found cheaper on sales (I got my Tirreno Tora helmet for $25, a decent pair of biking shorts for $25, a mini-pump for $10, a multi-tool for $10, and a saddle bag for $10; all from sales from my local bike store). Some will also say you need shoes and clipless pedals, but you should be OK for a while with the straps and regular shoes. A cyclocomputer also helps, but is not 100% necessary IMO. So you should be able to get going for around $750, especially if you cn bargain for some of these items to come with your bike purchase, or even ask for a discount on the accessories when you are buying the bike.
Buying used is also a great idea, but make sure you do your homework on frame-sizing before you get a used bike. A wrong-sized frame can make riding very uncomfortable, and sometimes short test-rides aren't enough to determine if a frame fits properly or not. So make sure you have a good idea what size frame will work for someone your size before you get a used bike. Another good thing with used bikes will be that you can save a lot of money in most cases, and that means you won't be out of too much money if you find out biking is not for you. Good luck.