The Lite is largely a poor choice, unless you only want to play in handheld mode. If you want to share with others, I mean, you can, but you'll need to find a way to balance the Lite on a table since it has no stand. Then you would have to get some joycons or other bluetooth controllers and sync them to the system. It can be done, my kid until she accidentally destroyed it has a LITE and I linked my pro controller to it a few years ago to play a game with her on the couch.
She currently has an OLED basic white model. It has far more durability than the standard switch, but nothing is quite as tough as the lite as it's thick and just one big chunk of a handheld.
You said you have a loaded up tv as a concern, you also seemed concerned about game prices? Personally unless you have to buy a new one, look at the second hand market for an OLED Switch complete in the box that looks lightly used/cared for. You can buy them for right around $200 which is HALF OFF the current price of $400 due to the memory/storage shortages caused by the market. Switch Lite you usually end up paying $100-120 used, seems kind of dumb to cut yourself short.
If those game prices scare you, most switch games even new top out at $60 at retail, but on the bottom end new can be $20 at retail too. Again if you would be willing to buy gently used second hand games, you can get most Switch games you'd likely care about for $40-50 at most, as cheap as perhaps $10-15 (before shipping online.) If you are ok with digital, watch dekudeals.com or get on Nintendo store's update mailer as they do daily, weekly, monthly, holiday and special event sales where games usually are 25-75% off (usually 30-50% on the better loved stuff.)
Being a Switch owner can be pretty cheap very cheap against the PC, Sony, MS and even Switch2 market too.