I will be putting it on a bookshelf that is 7.5" deep x 30.5" wide for the base of the tv. .... Any suggestions?
Find out the Maximum Weight Limit of the shelf - that sounds like a pretty skimpy stand.
Also make certain you can tether the top of the set to the wall behind the bookcase, to help prevent it falling face forward on to your floor.
At 10.5 feet, and ASSUMING a diagonal screen size of 42" Or Less (perhaps 46" for a thin bezel unit - ??), 1080p won't be Critical.
Unless your vision is unusually acute, a 720/768p panel will suffice.
However, a 45-degree angle could be enough off-center to impact the PQ of SOME LCD panels - with Edge-lit ones being the most like to have problems.
That, at least, is something you may be able to check out yourself with a visit to a local store. Simply walking up & down the TV aisles will show that some LCD panels do a pretty good with off-center viewing, while on others the PQ falls off Rapidly....
Obviously you will need to find a stand that will fit your 7.5" depth, with is likely to be more of a problem than the 30" width - but you'll want to measure both, to be on the safe side....