You're going to want your new TV to support 4K (and HDR if you can swing it), but the game itself won't be broadcast in 4K. The upcoming 2018 Winter Olympics, however, will have 4K content to consume.
Buying a really big, really cheap TV won't get you a perfect viewing experience. You're likely better off buying a smaller, higher quality TV, than going purely on size.
Once you get your new TV, set aside some time to tweak the picture so it looks its best. Here's a guide to get you going.
This isn't a TV, but rather an HD antenna that will let you watch the game for free if you don't have cable! (Amazon)
Samsung 55-inch 4K QLED Smart TV $1,000 (Amazon)
Sony 60-inch 4K UHD TV $698 (Amazon)
LG 43-inch 4K Smart TV $379 (Target)
Visio SmartCast E-Series 70-inch UHD TV with HDR $1,079 (Target)
RCA 78-inch 4K TV $1,299 (Walmart)
Samsung 55-inch Curved UHD Smart TV (Walmart)
TCL 55-inch 4K UHD Smart LED TV for $650 (Amazon)
Sony 55-inch 4K UHD Smart LED TV $998 (Amazon)
Sony XBR75X900E 75-Inch 4K Ultra HD Smart LED TV (Amazon)
LG 70-inch 4K UHD Smart TV $999 (Best Buy)
LG 60-inch 4K UHD TV $599 (Best Buy)
Samsung 65-inch UHD 4K TV with HDR $1,699 (Best Buy)