Actually that STUPID comment was bit more than i wanted to say... but just had to get attention cause other option which i consider unwise was so clearly winning
I have to say i dont know ATSC that well, but u have to excuse me since here in europe we have DVB-X system, where X denotes different transmission technique (c,t,s,h for cable, terrestrial, satellite and mobile).
Now i dont know if ATSC is just your terestrial standard in which case it would be like u said for OTA channels... purely NTSC-telly would need a separate box to receive terrestrial HDTV. I dont know much how ur cable and satellite systems work though.
Now about projector... Most people have this fear of projector... and they keep it up and keep buying inferior tv equibment. Is same behavior can be seen in organizations all the time economics even have term for it (resistance for change), its natural for human beings... u just have to get over it and u see clearly with CLEAR and BIG picture how silly u were.
If u dont belive me... ask around... Ill bet u only find few people who actually have made transiotion from tv to projector... But i promise u... u wont find a single person who made transition back from projector to telly.
Ive been using projector like ten yours now... in both really small apartment and quite big house. So i give u walktrough for few common myths based on my observations.
RESOLUTION
One of the biggest thing which set back projector pioneers was that afordable models ten yours back were ****ty. My first projector belonged to that gategory. I almost slipped back to being telly people. It was only because of resolution was weak... nowadays all projectors sold are atleast dvd quality when it comes to resolution. Even though picture was ****ty sheer volume of it made one of my friend projector convert.
SCREEN
Ok the screen can easily cost as much as projector or even more. But getting a screen is only important if u dont have suitable white wall, or cant for somereason to use can of white paint. Ok im gonna get flamed over this by ht purists. But i tell u with some experience that dollars invested to projector and can of paint than same amount invested to canvas and projector together will get u muuuuuuch further in terms of picture quality. I have experience of DIY canvas (my first solution) white wall (in bachelor box) and professional white screen (now, because i didnt want to paint over windows) and theres hardly any difference.... ok with painted u r gonna get as many sour looks and comments as i will get flames for this... but its just people usually have to find some faults of u new projector system... so they can happily continue miserable existance of telly people.
SETTING UP and ISSUES WITH FLAT
Ok putting projector operational is bit more trickier than carrying telly in... well atleast if lift is working

But good news is u basicly do it only once. Other good news is projector projector is actually more transparent in app than telly is... u have your white wall and little box on ceiling. Well ofcourse wall mounted plasma or LCD screen doesnt actually take lot space... but in small app where even inches count thats still more than projector, which doesnt take any useful space at all.
Modern projectors dont require calibration like old CRT-canons did, hardest configuration is actually getting picture to exactly place it belongs... this includes finding right place for projector in all three dimension (its easy just little math and experimenting) adjusting zoom and mayby tuning height... u need to get projector with wide enough optical zoom (this is especially important in small app) also heigh tuning is nice but not mandatory... many models are planned to be installed upside down ceiling and this case u might do without... feature is nice though. Dont let side projection crap fool u. That is done compromising resolution and comes with high pricetag. go for it only if orthogonical projection is absolutely unfeasible in your flat.
Obviously projector dictates some terms to ur organization of furniture and for the room... but its usuall rather lean... atleast one 4 meter wall without paintings for big picture

no lamps hanging on ceiling and deep enough room for projector lens to generate that big picture... this is when zoom comes handy in small app... Anyway i was living on student app on high land value area... so 1 room apps size was 26 square meters... and yet in that app i had 3.5 meter screen (oh thats not from corner to corner how they state in tellies but thats how wide pic was). so projector defenetely works in small apps and its SAF aint so bad as big telly have (well thats after they have seen it in operation... before that projector might be as scary as a word as vibrator).
FISHNET
Me like most of us are very fond of fishnet socks on girls... and that is where fishnet should stay... its not so nice on u picture... Sure u can buy DLP projector to avoid fishnet... but since HDTV projector is what u r after... i can promise u that u wont be bothered too much cause of fishnet even with LCD projector cause with that resolution fishnet is so fine. Fishnet is more problematic in LCD projectors with lesser resolution.
LIGHTING
This issue is mostly from CRT times too... modern LCD projectors come with so powerfull lamps that they can be used in bright class room... as long spot lights pointing on canvas arent on... Ok that enough for powerpoint... but for movies mayby u should turn lights of

if u want more theatrical athosmphere or are lucky enough to live very bright part of world u could think getting aluminium curtains which dont let light tru at all for windows... this is usually very small expense... depending amount of windows... only in case when u have huge windows... u might need to make them as custom work and price can sky rocket.
SHORT LIFE-EXPECTANSY
Projector gives u around 2000h of fun... then its ready to recycle bin. Its much like ink jets... theres absolutely no point to buy lamp... new projector is much more reasonable investment. Lamps cost almost as much for the projector as new projector of that or better resolution will cost on the day that ur lamp resigns. Is moores law applied to home theatre. Usually 2000h means 2-3 years... but ofcourse it depends on your viewing habits.... if u watch much more it might be reasonable to buy new lamp if ur original investment was unreasonably high
Ok this was much more than i was prepared to type to convert u...

I cant recommend u any particular projector... since i still have like 400h lamptime before is time for me to start looking... but if what ive heard from my friends about current state of business is accurate. I would say budget u mention is quite right for LCD HDTV projector... who knows mayby u even have money left for curtains and can of white paint.
Then again im defenetely projector people... hear what telly people have to say and make u educated decision. But in my hometheater theres only one use for 37" LCD telly... that is in upright position on wall as movieposter frame.... ok might sound arrogant... but if u take a look (ebay) how much is asking price for legacy posters... that comes just economical and practical