A Tele would actually be my first choice, but I've never actually owned one. Les Paul style guitars have very different playability because they're actually designed slightly different from most (I've been told this, I've never worked on a Les Paul). Where most guitars have the neck set flush or angled slightly up with respect to the body, LPs have the neck angled slightly down, with a raised bridge.
The input jack is a common failure on pretty much EVERY guitar. My Ovation (cheapest one they sell) is the only guitar I've owned that I've never had to repair the jack. Truss rod adjustment can definitely help get the playability there on your Tele, in my experience the entire Squier series needs (very slight) adjustment every few years.
Some more tips if you're going to give it a try: Pull back slightly on the headstock (bending the neck to tighten the strings) when making your adjustment, if you don't remove or loosen the strings. This will help remove tension on the inner mechanism, and make the adjuster easier to turn.I like to make adjustments with the guitar in tune, so you can easily check it with proper string tension. If the adjuster is stuck, work it back and forth until it turns easily. If the inner mechanism is corroded, this will loosen that mechanism up so you're less likely to damage it.
If you have all day to REALLY fine tune truss and bridge adjustment, maybe file a few frets that buzz too much, most Squiers can have feather-light playability at any fret, even with heavy guage strings. The problem with the Squiers is that they won't stay that way as long as the full price Fenders.
Yeah I'd like to take the time to actually learn how to work on it rather than take it to a luthier. I've always been the kind of person to work on my own stuff. I don't have any frets that are too bad with buzzing, but I could just be used to it too. The idea of filing them down scares me, but I have the tools to do it.
And yes, the Squiers vs. Mexican/American Fenders is all about durability. Any touring musician will tell you that a Squier simply won't hold up while steadily touring.
I tend to buy more affordable guitars because I just don't play enough to justify the $1000 price tag, but if I found the right guitar maybe.
Like I said next purchase will probably be a Epiphone Les Paul like my ex girlfriend had, but I also really want a double humbucker Telecaster(I think it's called the 1976 deluxe). There' also a Telecaster that has the Stratocaster style head-stock and at least one humbucker. I also really like the Jazzmaster, Jag-Stang, Mustang, and Jaguar Fenders, and they're all available in Squier releases now too :) I love the shape of those.
If I ever get another bass it'll probably be a Fender too.
And yeah, Les Paul's necks are set into a single piece of wood that widens out to become the body. Versus Fender's bolt-on necks. Fenders were designed as the first practical and efficient guitar to manufacture. With Gibsons a larger piece of wood was needed for each body, and a lot of it was going to be wasted. Fun fact: the original Gibsons used a wood for the body or neck(can't remember for sure) that's no longer available because the tree is a protected species now.