I have a Sharp Aquos that's been a good'n. Nice combination of performance and price. I don't use the smart apps. Decent 60" 1080p units from several mfgs are well under the $1k mark now.
I run my Netflix/Youtube/Streaming Whatever throught the XBox. App performance is much better and the menus are far more intuitive.
If you're springing for a new TV, spend an extra $80 and get a BluRay player. Direct hookup to the new TV, upscaling for much better picture with DVDs than using a dedicated DVD player, and now you can play them new fangled bloo rey thingies. If you need to keep your VHS/DVD player for other reasons just make sure the TV has at least one set of RCA inputs. They'll be called omponent/composite in the specs.
Consider having a ground run to the outlet feeding your TV location. The price of installation is far less than replacing a bunch of electronics. Get a real surge protector, not a jickey $5 power strip. Tripplite Isobar is my preferred brand and model.
Finally, don't buy hookup wires/cables or surge protectors at a retail outlet. It's hghway robbery. Amazon has AmazonBasics and Monoprice brand cabling for a third of what Big Box charges.
What size and budget? With that we can give some recommendations.
Maybe something like this? Toshiba 55" LED with the inputs you need and sans all the Smart App (i.e. "more expensive") foofery you'll likely never use. $550 and you even get to keep the box.
http://www.bestbuy.com/site/toshiba-55-class-54-6-diag--led-1080p-hdtv-black/4203600.p?id=1219707771149&skuId=4203600Or bump the price a bit to $750 and get a 120Hz refresh rate for better clarity during high screen activity. It's currently on sale for $600. (At the sale price I recommend stepping up to this unit for the added clarity even though you likely never use the smart apps it has.)
http://www.bestbuy.com/site/samsung/6010007.p?id=1219657153378&skuId=6010007Edit to add... they also have a Vizio 55" true 120Hz refresh rate set for $559. Doing this on my phone and copying links is a pain.
Brad