Welcome Jack
Although the K-series is a characterful engine and less problematic than folklore suggests (and can be easily tuned), I'm still going to vote for the Yota engines. No HGF to worry about (they still can fail on the K), no cambelt to change, and I think that the gearboxes have a nicer (more slick) change.
The 134bhp 'S' is the same 1.8 engine and 5-speed box as the pre-facelift MR2, both are bulletproof in the Elise, problems are extremely rare. I reckon that this Elise is perhaps the most underrated of them all, it's perfect for road use.
The 189bhp 111R is the same 1.8 engine and 6-speed box as the Celica 190. Engine is brilliant, the cam change at 6250rpm (can be lowered to 5500rpm with a ECU reflash) is addictive and the car feels FAST. The gearbox is nice to use but the syncro in 3rd gear is a bit weak - it can feel a bit notchy when the car is cold. Still, very few actual failures on standard 189bhp cars.
Depending on budget (i.e. more money!) there's also the younger (2010 - 2016 I think?) 1.6 Toyota engine in the S3 bodyshape. I love the clean lines of the S3 and the cars in general are less rattly/squeeky and a bit nicer inside. This engine is unbelievably frugal and although it's not very torquey it's still fast enough if it's driven hard.
A couple of generic points;
the roof on an S2 or an S3 is much quicker and easier to operate than on the S1 (and the early 'longtail' S2), although none of them are anything like as easy as on your MR2 😄 , and, the sills on an S2 (and S3) are a bit lower than on an S1, making it just that little bit easier to get in/out.
They are all great cars, a few little points to watch out for and don't think too much about age/mileage - buy on condition.
Finally, if you're going for as spin in Dean's car don't forget to wear brown trousers 👍
Cheers.