You're looking for something along the lines of the Asus VW246H. It has full HD, a multitude of inputs, built in speakers (whoopee?) and is MLG certified. Asus makes extremely good monitors that are built with gaming in mind (think PS3 & Xbox 360) and are much better than the average monitor.
1. LCD or LED?
both are actually lcd. the ones labeled lcd uses ccfl backlighting while the ones labeled led use led backlighting. both are around equal in performance. led saves a bit of money on your power bill but cheap monitors using led can have a blue tint to them. higher end monitors using led backlighting will not have this. the reason is the leds used are different.
2. How many inches would you recommend?
for a computer monitor 22-24" is a good range. if you sit further back then normal then a 26" might even work. i use a 40" television from a few feet away and it works fine. chalk this up to personal preference. go to a store and judge sizes and distances to see what you like.
3. TN or IPS panel?
depends on your personal preferences. most gamers will say a 120hz tn panel hands down if you can get over 60fps in a game. 120hz tn panels will give you a slightly smoother playback but tn panels are known for having rather bad viewing angles. certain screen coatings can improve this. ips panels in general have almost 180 degree viewing angles without this effect. they are not available in 120hz (only 60hz) but i do not see this as a problem. buying an 8bit ips panel (s-ips, h-ips, p-ips) over a 6bit ips panel (e-ips) will give you a higher color accuracy then all of the other panels.
4. What resolution would you say ?1920 x 1080 or 2560 x1440.
1920x1080 is most common and if you use this resolution 1080p video will look the best. your hardware will also be able to handle maximum settings in games for a longer period of time due to the lower processing power required. due to the pixel pitch on 2560x1440 monitors not being any higher (and in some cases lower than 1080p models) you will not see a sharper image unless you sit back from them. where a 2560x panel really shines is when multi-tasking or doing professional work.
i would not suggest a monitor with speakers. typically the speakers are crap and you will disable them anyways. save your money and eliminate this feature.
dvi or hdmi is fine. for ease of use pick one which matches your video card. or if you have a ps3 or other device to hook up also then pick hdmi so that you can use a hdmi splitter or switch. remember for a ps3 hookup you need hdcp-compliancy.
asus, acer, dell and viewsonic all make good monitors. in monitors i personally prefer viewsonic professional monitors (ips panels). if you have no budget then perhaps a lcdtv is not out of the question. in which case go with a 60hz (NOT 120 or 240 for good reason) sony or samsung.
60hz or 120hz? tn or ips? panel size? this depends on your own preferences. see the reasons i listed.
led or ccfl? i would say ccfl unless you buy a high end monitor in which case led would work. led would also work for a tv. or if you are power concious led and try and adjust out a blue hue if you see one.