How big of a budget 144Hz are we talking? If you are looking for a bare bones, 24inch 1920/1080 monitor with a quick response time and 144Hz, get the Dell S2419HGF 24. It isn't by any means a top tier gaming monitor but with some color adjusting and making some changes to some of the settings, it is an excellent budget gaming monitor. You'll get a full 144Hz Monitor with changeable response times (5ms, 3ms, 1ms). I grabbed one on sale for 220$ CND and for the price, I was not disapointed.
Rule of thumb for buying a monitor: Find one you want and wait for it to go on sale. It will happen, you just have to be patient