Which engine is better depends on what you want. The 2.0 is known as a reliable, but rather uninspiring engine. The 1.8t gives you considerably more power, and still gets pretty good mileage, but has some reliability concerns. The VR6 is similar in performance to the 1.8t, maybe a little stronger in stock form, but gets worse gas mileage. The 1.8t is also cheaper/easier to mod, as most turbocharged engines are.
Between the three you've mentioned, I'd choose the 1.8t because it has decent performance and is fairly economical. I'd prefer the
TDI over any of them- but of course I would, because that's what I drive.
As far as doing a swap, I don't think that's something I would want to do. Unless you happen to find a cheap engine from a wrecked car, and have the time and tools to do the swap yourself, I think the best option is to find a car with the options you want, and drive that. As far as making the 2.0 faster, I don't know a lot about it, but generally, to get a significant power increase from a small, naturally aspirated engine, will probably cost a lot of money, and leave you with a car that isn't very comfortable in daily driving.
I'm not sure how many miles to expect from the 2.0, but any modern engine should last at least 200k miles if it's properly maintained. It's the rest of the car that worries me.