I'm just a measly no-nothing but I believe competitive times at a regional now are around 2,500 hours total with 600 or more multi. But it varies widely. Basically it's very difficult to find a job. I think you'll have to teach for 4 or 5 years to get your hours; and that is only if you get to instruct in multis frequently (which is very rare). Maybe going to ATP and trying to snag an instructor position is the way to go. Or maybe MAPD. Or maybe, as many suggest, you should just work your way up the instructor chain and eventually find an FBO where you can teach multi once in a while; and hopefully help the owner fly multi charters. Keep researching all the web resources available; all this info is available.
It depends on where you go. Keep your eyes open and update regularly once you meet an airline's minimums (usually around 1200tt and 200-300 multi). Also, work on networking. CommutAir, for example, recently hired a number of instructors with <1200 tt. They did almost universally, however, have recommendations from current pilots with the company.
Also, if you limit yourself to flying for the regionals, it could be a very long wait. Look into other options, once you meet 135 IFR PIC mins, start applying to the freight operators, charter companies, etc.. 1-2 years of instructing should get you those mins. Planning is important. Keep in mind the industry is very dynamic. Keep a close eye on the hiring trends. Apply early, apply often. Flexibility is key, if you are able to relocate, many more doors will open for you.