Actually I might just use this current PC as a little personal computer for files for work and projects and such, while I build gaming PC from scratch and hook it up to my 34-INCH that my Consoles are hooked up to, which I know gets 1080P. I know others do that as well. Itll save me on getting o new monitor, would that work?
I hate to be Debbie Downer here, but I'm trying to be real with ya - are you sure your 34 inch TV is 1080p? Cuz that's a really uncommon TV size and I'm guessing its older. Could just be 720p(or HD-Ready as many of them call it).
I would honestly recommend waiting a bit and saving up some money to do this right. First thing I'd recommend is buying a proper 1080p TV, assuming I'm right about your 34-inch not being 1080p and that you want a living room PC and not a desk monitor(which would actually help you as 1080p monitors can be had for pretty cheap). This will probably take up a majority of your current budget, but you will at least be set from there on, whether you press on with a gaming PC or change your mind to get a next-gen console.
Next, I would definitely say that saving up for a new gaming PC is the right thing to do. It wont be cheap when added in with the cost of the new display, but a new CPU, GPU, motherboard, RAM and harddrive will all add up to be one massive fucking upgrade over what you have now. And if you just wait a few months and save up, you'll likely have some new GPU's to pick from offering even better bang-for-buck.
Of course, if you're reluctant to spend that much more after buying a new display, nobody is gonna knock you for settling for a console, either. If you're on a budget, it may just be the more economical option in the short term. I still highly recommend doing what you can to get that new gaming PC if at all possible, but I realize that may not always be financially feasible.