I know it doesn’t mean it has to be wall mounted, but I did read that one reason it is desirable is that the wall mounted tv doesn’t have a tangle of cords running down the wall. Just was saying I don’t care about the tangle of cords. 
I’m wondering if my existing DVD player will still connect.
Your existing DVD player will most likely connect. We also have a Samsung smart TV, and it has a bunch of connectors of different kinds. We’ve had no problems with it. We also have a Panasonic plasma which has worked fine for years, but it sure is heavy. Can you even get a plasma TV anymore?
You probably want your new TV to connect wirelessly to your home computer network (if you have one), so you can stream Netflix, YouTube, etc., easily. There were a couple of services we wanted to stream that the Samsung doesn’t support (i.e., Crunchyroll), and I use a Chromecast for that. We’ve discovered that we watch YouTube way more than we expected–much more than regular TV channels.
One note on smart TVs, you can only access the apps that manufacturer supports, we bought a Toshiba 5-6 years ago and when the firmware updates, the apps have changed, we actually just use a Roku box with it as we cannot access things like HBO GO etc via the smart TV apps.
Are you talking about wireless as in wifi, or wireless as in a remote connection box? Most current smart tv’s probably have wifi built in along with apps like Netflix, so you’d use that ability to watch Netflix instead of plugging in your wii. The remote connection box is a high-end feature you don’t need, based on your posts.
It sounds to me like OP is complicating things. You just want a basic TV with inputs for your wii and DVD player. Just look at the outputs for those devices and make sure any TV you’re considering has matching inputs. If you’re really just using the wii for Netflix (I used to do the same) you can probably ditch it if the new TV has wifi and Netflix built-in, or get an Amazon fire tv stick for $40 since IIRC the wii connectors are obsolete and you can eliminate some clutter.
Also make sure there’s an appropriate connection for your cable box, or whatever else you’re using. HDMI is the standard these days so I would 99.99% say every TV is going to have one or more HDMI inputs.
Other than that, you don’t need OLED unless you’re a huge movie buff who cares about a perfect picture. You don’t need 4k in a set smaller than 50". There should be a zillion <50" LED tv’s in the $600 and under range, as that’s the sweet spot for price right now. Don’t over-complicate it, just buy a brand you recognize at a price point you like once you’ve verified all the inputs you want are there.
Theoretically I also use the Wii for exercise games. 
I need to figure out if I’m going to keep doing that.
Bought my dad a smart TV through Sam’s club and the cable guy came and set the whole thing up (has a cable box) showing how everything worked. Great experience.
We have a couple of large Samsung TVs which are connected to a cable box and an Apple TV. We needed one more for a different room and the store was out of normal TVs so we got a Samsung smart TV. The Samsung smart TV was so bad that we eventually got another Apple TV box to connect to it – much better. I would skip the smart TVs and go with AppleTV via the HDMI interface. I think that @somemom pointed out a similar issue in post #22.
One thing that I like about the newer Apple TV boxes is that they allow my normal Apple laptop to “grab” the TV, so that anything that I can get on my laptop I can also display on the TV. For example, this can be used with youtube music videos.
Our old VHS / DVD player connects via the old three plug RCA connectors.
The picture quality is “VERY Good” when we are watching via the Apple TV (sometimes Netflix, sometimes HBOnow, sometimes PBS) but only “good” when watching via the cable box. The sound is okay but a bit disappointing when watching concerts or Elementary (where we find the accents a bit hard to follow).
I’m sitting at work right now LOL. I bought a 48" LG Smart TV a few months ago but had no idea of its capabilities, I was (and continue) using it just like my televisions from a decade ago. A friend came to visit and loaded it up with her Amazon, Hulu, and Netflix accounts because she and her kids spend loads of time using my home during rainy weather when they summer close by in a small camper and several short vacations during the rest of the year. I have figured out how to watch some Hulu shows and some Netflix shows but the rest is still vague to me. The above responses have really alerted me to the fact that I am so far behind the times. HDMI, connectors, TV wifi, oh boy…once winter weather arrives, I’ll sit down and figure it out I guess haha.
On the upside, I binged Orange is the New Black, Handmaids Tale and many seasons of Call the Midwife so I could get used to this.
Also don’t forget some credit cards will extend the manufacturer’s warranty. I think my cc added a year or two. What I liked about my CC is that they kept the receipt for me so I didn’t have to worry about showing proof of purchase 3 years later. I called them up when I bought my tv and they had me email them a copy of the receipt so they’d have it on file if I ever needed to make a claim. I think Samsung actually did need to make a repair in the first year or two, but other than that the set’s been perfect for the past 10 years (it’s a plasma though, not LCD/LED).
It’s also great if you are a sports fan. ESPN 3 has not only live streams but replays of everything. Though I could get it on my iPad it’s so much better watching it on a 50” TV.
Having a TV with all the bells and whistles also means only needing one remote!
I believe Costco gives you an extra extended warranty on electronics they sell.