With that budget, I wouldn't consider any bumper-mounted spare tire carrier, I'd instead go for the spare tire carrier from Offroad Fabricators at http://www.orfab.com/applications.ph...ers&Active=Yes
which supports the entire weight of the spare tire via hidden brackets that bolt to the rear rollbar bases. It doesn't get any stronger than that.
I've run that particular carrier on two different TJs with no squeaks, rattles, or even the tiniest amount of sag. Its mounting strength coupled with it being supported by three support points, two when open, compares favorably when compared to a bumper mounted carrier that has only two support points, with only one support point when open and the second point being more to simply hold it latched shut and less a support.
Also, my first ORF was also holding two always full heavy jerry cans in addition to its 35" spare tire and not even with that much weight did it ever sag over its ten year life before that Jeep was stolen. On my second ORF carrier, I went with the model that doesn't carry the jerry cans since it doesn't stick out as far. It is so strong than when you swing it shut, it consistently swings directly into its driver's side latch with no need to lift it so it seats. Thats with many years of use on two different ORFs.
Not to mention with the ORF carrier you can run any bumper you want since it doesn't even touch the bumper. The ORF together with an aftermarket bumper of your choosing will easily be under your budget price.
A good discounted source for the ORF bumper is Savvy Offroad