Fair warning: this is my opinion and worth what you paid for it. You'll get plenty of others, and they'll probably disagree with some of the below.
Your budget really is going to help define what you get. $500-700 is a decent budget, but I assume we are talking soup-nuts here, not just the irons? So you need, at a minimum:
Bag
Driver*
3 Wood
Irons
Wedges*
Putter
Now the above *'s may be something you can skip. You are only going to hit a driver 12-14 times in a round (and that's probably too many times) and for most people starting out a 3 Wood will do just as well. And as to the Wedges, it will depend on what kind of iron set you end up with. If it goes through SW then I would skip picking up anything else, but if it stops at PW or GW/AW, I'd look at picking up a sand wedge.
I would spend most of your money on the Irons. They will make up the majority of your shots on the course. A good set of brand new, brand name irons will go EASILY $500-700 by themselves. I would suggest looking for the best set you can afford from a major manufacturer looking perhaps at last year's clubs where they are still available. There is no substitute for hitting the clubs, so try to find some places that will let you take some clubs with you to a range to hit. It's great if they have one of those simulators in the store, but it's really not a substitute for hitting them at a range OFF GRASS. NO MATS.
Once you've decided on your clubs, don't forget that most manufacturers have "Certified Pre-Owned" sites where they sell their clubs used from barely to well-used. GlobalGolf.com is a great site for that and open box deals (significant savings on never hit clubs). Be sure to save some cash to get them fitted as well. That can be the difference from an OK set of irons to something that really works for you.
Don't go spending a ton on a putter. It will be the club you hit the most strokes with during a round, but putters are a very personal choice and different putters work for different people. In my most humble opinion, you will not notice a big enough difference from a putter you pick up at Play It Again Sports or somewhere like it and a brand spanking new $200-300 putter off the rack at a golf store. Find something that works for you and go from there. You will likely change your putter multiple times if you are like most out there. Drivers and putters seem to be the two clubs that get turned over the most. It's always the equipment that's the problem, ya know?
Driver/Three-Wood. Find a way to save money here if you can. You don't hit enough shots with the Driver for it to take up that much of your budget right now. For most people starting out, the Driver is just a source of frustration anyway. Again, look for used or open box or last year's close-out deals here.
That budget starts shrinking substantially when you start looking at all of the above, and I haven't even mentioned balls (lostgolfballs.com!) or golf shoes.