currently i use a 32" monitor myself
define casual gaming ... PC gaming or console gaming? if console gaming you wouldnt notice between 720 and 1080 on an xbox, but you may on a ps3 especially with blu-ray quality and some of the new gamers.
Pc gaming you wouldnt notice - plus i assume these are older games you're playing anyway, if you were playing the new stuff doubtless your gcard would have a hdmi output
the hz rating is great if you play alot of fast action games or watch alot of sports. back in the day that was the selling point of plasmas over LCD tvs, but for casual i dont think it really matters though quite alot of smaller tvs are 100hz anyway.
yes you can use a HDMI - DVI convertor and no, theres no quality differential as they are both digital, you'll lose audio ofc and if you ever switch between the two, i mean i noticed hdmi handled colours a tad better but i didnt really care as it was un-noticeable.
personally, i love LG tvs - they have great tech and last forever with the right care. samsung tends to get a little pricier for the same tech and the sony bravias really suck these days.
thats my 2 cents
- currently using the 32inch LG