I daily a 1980 300TD. Yes, the 'T' stands for 'Touring', which means wagon, not 'Turbo', as most seem to think.
My 1980 is non-turbo. In 1981 the Turbos came.
The turbo cars got a taller rear end, which makes for nice cruising, but from a dead stop honestly I couldn't tell much difference between my car and a turbo 300TD I drove once. The turbo lag on these is very apparent.
The HVAC systems on these cars are the worst. Mine makes heat in the winter, and that's it. The A/C takes a crazy amount of money and time to make work right. I think the later W123's are slightly less complicated (W123 went through the 1985 MY) but still problematic.
They rust, seat springs wear out, and the SLS requires a bit of maintenance. I know everyone says the valves need setting every 15k but I've never touched mine, and the car runs excellent. I think with modern oils, and frequent changes, they shouldn't need much adjusting. I run 15W40 diesel conventional oil, changed every 3 months (about 3k miles, my odometer's broken). The Wix filters, surprisingly, suck. Stick with Mann. Change the screw-on fuel filter once a year and the little plastic fuel filter every other oil change.
Odometers on these cars are known to fail, question any mileage unless substantiated. That said, there's one on CL now with 440,000 miles that seems to be in very good condition. Most mechanical parts are cheap and easy to replace. Brake pads are like $12 a set, for example.
I have bundt wheels on mine, never heard they were indicative of a turbo. When the tires on there now wear out I have a set of W126 15" wheels I plan to swap to. I picked these wheels up for $50 for 4. It's a common swap to get access to better rubber. Which you need- it's all about momentum with these cars.
As I said, I daily mine, and you just have to plan your maneuvers. Forget passing anyone on a 2 lane road unless it's a farm tractor. I have pegged the speedometer at 85 mph, so it will hustle, and the engine (unlike stereotypical diesels) loves to rev. I also only feed mine 50 cetane diesel, and a little DieselKleen additive. It idles very smoothly- about like a 4 cylinder from a 318i BMW.
Transmissions can be problematic. Make sure it shifts correctly. The adjustments are finnicky, and if it doens't shift properly it can require a foot lift to upshift or upshift waaay too early and very softly. Of course, the soft shifts will wear the trans out in very quick order. Make sure your Giubo (rag) joints are in good nick, too, or you could toss a driveshaft.
TL;DR version: Find one that's not too rusty, buy it, maintain it, drive it till the sun peters out.