You honestly don't need 1080p for most games at a distance, but you're in luck as here's a 32" Samsung for exactly $199 [https://www.amazon.com/Samsung-UN32J5003-32-Inch-1080p-Model/dp/B00V0923TG/ref=sr_1_1?ie=UTF8&qid=1467726162&sr=8-1&keywords=1080p].
At that price you're not going to have a high refresh rate. It'll be 60 Hz. With TVs at that range you're also going to get screen tearing, which is hard to describe. It's not the end of the world.
At least it has two HDMI, one coax, and component, which also doubles as composite for any older console systems you might have.
Newegg [http://www.newegg.com/Product/Product.aspx?Item=N82E16889354950] has it for slightly more at $227, but they provide expedited shipping.
Note that the TV doesn't come with an HDMI cable, but you probably have a few of those lying around. If you're going to buy one, don't pay more than $10. Here's an AmazonBasics [https://www.amazon.com/AmazonBasics-High-Speed-HDMI-Cable-2-Pack/dp/B00L3KNWBU/ref=sr_1_3?s=aht&ie=UTF8&qid=1467729167&sr=1-3&keywords=amazonbasics+hdmi] one for $8.99. It costs a little more because it's 9 feet long. Here's a cheaper one [https://www.amazon.com/AmazonBasics-High-Speed-HDMI-Cable-Standard/dp/B014I8SSD0/ref=sr_1_1?s=aht&ie=UTF8&qid=1467729167&sr=1-1&keywords=amazonbasics+hdmi] which is 6 feet long. And if you're going from DVI to HDMI, I have one of those cables and it works great. The Amazon Basics [https://www.amazon.com/gp/product/B001TH7T2U/ref=oh_aui_search_detailpage?ie=UTF8&psc=1] line hasn't let me down yet. That's for a DVI-D/I to HDMI connection.
Don't forget that using DVI from a PC means you still have to find a way to get sound out.