Guys, guys, guys....the man said he wants to renovate, not rip out and replace. Every recommendation given so far is for equipment that would be required to create a new lawn from scratch, not work with what is already there. Not only that, but investing in that kind of equipment isn't a wise investment, unless you're going into the business.
Here's my advice, Hilden, and it's not only what I suggest, it is what I have done personally. You need a core aerator. Few things will revitalize your lawn like core aeration. It is an implement that you will use at least a couple times a year from now until you give up. The next thing you need is a topdressing spreader. Broadcast spreaders won't do (you may need one of them, too, at a later date). A topdressing spreader (or topdresser) will spread a uniform layer of any material on your yard. I topdress with compost a couple times a year and sand at least once. There are lots of different styles in a wide variety of price ranges, but those two items can be had within your stated budget.
Aerating and topdressing will eliminate the compaction in your yard, prepare the site for overseeding (easily done by hand) and eventually smooth out the humps and bumps and dips. They are long term processes that you need to repeat a couple times a year, every year, so owning the implement makes good sense.