Reliable and sturdy, but still fun to drive.

Oh, man. You've got a lot of options.

To start; yeah, you're on the right track looking Japanese. For your criteria, I don't think I'd look anywhere else (except for maybe a Pontiac Vibe GT? but that car cheats by using a Japanese engine and engineering).

Secondly, if you're serious about that 10 year old/125k miles restriction, that will restrict you to only the mass market, non-luxury Japanese vehicles. Among these, A Mazda 3 is generally acknowledged to be the most fun to drive. You can get the 2l engine version for better reliablility and fuel efficiency or the 2.5l for more power. As a side note, a stock late 00's Mazda 3 with just the 2l engine has almost exactly the same 0-60 time as a stock v6 late 80's early 90's Mustang/Camaro/Firebird (like 9 seconds, manual transmission). You should be able to find a well kept late 00's Mazda 3 with under 125k for a bit under $6k. I'm honestly not sure if there any newer RELIABLE cars with better performance that you'll be able to find within your budget. Certainly there are turbo VW's (or even the turbo Mazdaspeed's), but those are so much less reliable.

If you can relax the 10 years/125k miles thing, there are a lot of interesting options that open up.

Lexus made some nice cars in the late 90's/early 00's. The IS300 and the SC300 are fabulous cars; the 3-liter 2jz inline 6 is a beast of an engine; they're RWD even. For a few grand you can turbo them for huge HP gains; stock internals even. And if you want V8, RWD, there's the SC400 (for my money, I wouldn't, but you could).

From Acura, an early 00's RSX's; even the type S would be in your price range.

For Hondas you've got the Prelude; especially the SH for more power.

Infiniti G20's (a little older, less powerful, you'd be able to afford a super nice one) or G35/G37's (newer/nicer; you'd only be able to afford a higher milage/thrashed out one) could also be worth a look.

So that's a lot of options. Honestly, if I were to make my short list from all these cars to definately check out, I'd probably start with a Mazda 3 and a Lexus IS300. Test drive one of each from a meticulous, knowledgable owner; learn about the cars, and go from there. They're both reliable; not-crazy-performance, but not slouches either.

I'll stick with the V8 cope theme.