If you pick up a good 720P or 768P (Sony's strange standard) set, there should be no screen door effect in that size. It really only starts to be a big problem at 50 or 55 inches. I have a 42 inch Sony in the bedroom that has no detectable screen door from about 3 feet on out.
If you do have a lot of light, then most plasma's are probably out. They tend to have very shiney screens (glare), and you can get to watch yourself in the TV, instead of what's on the TV (go to Best Buy one day and see how many Best Buy banners you can count in the TV)
Depending on how much room you have, one of the "table top" rear projection TV's, like one of these, should work pretty well for you:
Sony's KDF series 42 inch for $ 1,299 plus ship has excellent resistance to room lighting:
http://www.onecall.com/ProductDetails.aspx?sHist=12-2,3-15&id=28433
same model also available at Circuit City for $ 1,399:
http://www.circuitcity.com/ssm/Sony-42-HDTV-KDF-E42A10-/sem/rpsm/oid/130219/catOid/-12870/rpem/ccd/productDetail.do
Phillips makes a 42 inch LCD just outside that price range:
http://www.shopsunshine.com/item.php?item_id=18475
Toshiba has a pretty nice 42 inch for about $1,300-ish:
http://www2.buydig.com/shop/product.aspx?omid=113&ref=dealtime&utm_id=9&utm_source=Dealtime&utm_medium=cpc&utm_campaign=TB42HM66&sku=TB42HM66
Phillips makes a 50 inch plasma with an anti-glare coating (haven't seen the quality, so can't guarantee it) that runs about $ 1,800 from their outlet store:
http://www.outlet.philips.com/b2c_redesign/b2c/productdetail.do?productguid=4328965C3ACA008E00000000828BD47243A5ECC8562B019900000000828BD4B5&productarea=4328965C3ACA008E00000000828BD472&scenario=catalog&shop=OUTLET
All of these models have the built-in HDTV tuner that BEF recommends and will suit you pretty well into the future, even if you buy a bigger main TV somewhere down the line.