most televisions are 1920x1080p resolution (with the exception of the brand new 4k televisions and older 720p televisions that is).
honestly there is no real difference in quality betwen dvi-d and hdmi. the two are comparable and there are adapter cables available to convert between the different pin arrangements. in fact i personally use a dvi-d to attach to my hdtv (see link in sig for setup photo)
yes, some televisions are cheaper than the dell 3011 which normally hovers about $1000 (i've seen it as low as $850 and as high as $1200). they are all going to be no higher than 1080p or 1920x1080. they also arent guaranteed to have an ips screen which is highly color accurate like the 3011 has.
what are you planning on doing with your integrated (onboard) graphics? it should work fine for 1080p streaming videos and even 2560x1440 performance should be adequate for playing video content. however... its not going to play any games. at 1080p you might manage on the lowest possible settings but at 2560x1440 i would doubt anything will run smoothly even on lowest settings.
integrated is also not ideal for photoshop, video editing, 3d rendering, etcetera. however if all you do is email, office, youtube, play dvds, etcetera then it is sufficiently fine.
with that said... back to the monitor/tv side of things.... many people like using a large tv because it allows more of a multimedia experience. you can play movies and steam from the web onto a large screen which is more ideal for watching content than a tiny computer screen. some people such as myself like to play games on the large screen as well and it really works out great if you have one tv/ht system which has many things connected (such as a ps3, dvd player, computer, etcetera). for getting actual office work done though a monitor is best since the higher dpi (more pixels per inch due to the screen being smaller) makes things clearer and a bit easier to read at times.
i find a monitor more productive since its easier to read.
i find a tv better for video and entertainment since its larger and more immersive
thats the short version of things..