Anton
Welcome to the board!!
In answer to your question - liner or paint
There are two schools of thought here. Some people like liners 'cuz there easy to install, hold up even in the sun (provided you use 45 mil EPDM material). The downside is in a square pond you will have folds to deal with. It's not too bad if you make one fold along each wall from the corner and tuck the excess material of the fold in behind the main piece of liner. That way you eliminate all the wrinkles from view. You will need to be present as the water fills to make sure you can work on the folds. Start with about an inch of water in the bottom and work out the wrinkles on the floor. Any more water than that and you'll have a helluva time getting them out - you could damage the liner!!
Then work on keeping your folds tight and in the corners. The eventual weight of the water as the pond fills will compress the liner flat against the walls. You'll need to put some sort of "cap" on top of the pond to hold the liner in place.
Now on to paint - there aren't too many products out on the market that will give long lasting results. After just a few years(or maybe less) they start to peel and chip.
There is a new product on the market that I just became aware of today. I saw the ad in Koi-USA. Spoke to them and checked out there website at
www.pondarmor.com. It's called Pond Shield. Looks like it will do the job you're seeking without the extra expense of Polyurea spray. Comes out to about $2 - $2.50 a sq. ft. You can do it yourself pretty easy. Check out their website - they even have a few videos you can watch about application and product.
Good Luck
Mike