With monitors, you're almost always guaranteed to get less than 20ms input lag. With TVs, you're lucky to get below 30ms. On the contrary, it's more common to get one with 50ms or more. As such, you should always first consult reviewers. Unfortunately, reviewers usually seem more interested in the higher-end models, which your budget won't permit. Therefore, no applicable reviews.
Best bet would be to search youtube for user reviews. They probably won't have any accurate readings for input lag, but will possibly give a general opinion on how their particular model copes for gaming.
I used to recommend hdtvtest.co.uk for HDTV reviews with input lag measurements, but they've totally went to the wrong direction with regards to the budget. This year, the average price for their reviewed models is £3176, with only ONE model going below £1000, and even that was £950.
Anyway, currently I wouldn't even recommend a HDTV for gaming, even if you could find one for a reasonable price. FreeSync/G-Sync seems to be the game changer, and until it reaches the TVs, I wouldn't recommend HDTVs. Especially the FreeSync seems to gathering market share, and because it's an industry standard, it will become even more ubiquituos in the coming years. On the other hand, those features won't affect console gaming. So, if you don't intend to game much on the PC, then a HDTV should indeed be a worthwhile consideration for the current console generation. Assuming you find favorable reviews, that is.
But also note that currently the monitor market is riddled with bad quality control issues (bleed, glow, blur, etc.), and if you send the flawed unit back for exchange, you will probably get back an even worse unit. From what I've understood, HDTV market isn't riddled with these sort of hardware issues, but more with firmware/software side issues and bugs. In addition to the input lag limits. Philips seems to be a poster boy for all these. During my visits of the 2012 subforum, I've noticed that all the other subforums are also crowded with people having problems with their sets. Some people managed to change their models to a newer Philips model, only to face the same problems again.
Conclusion:
1) If you want to gamble, go for a HDTV - you might get lucky
2) If you like to play it safe, go for a run-of-the-mill monitor (preferably FreeSync/G-Sync)
3) If you want to waste money and get an inferior product, go for a Philips