Alternatively, if you just want to get the water marks out of the wood: Set an iron to warm (not hot) and allow it to heat. Lay a cotton napkin or tee shirt over the water stain. Iron the stain through the cloth for 5-10 seconds, then remove the heat for 20-30 seconds. Repeat as necessary, buffing lightly with the cloth after every 2-3 heat cycles. A hair dryer may used instead of the iron. Set it to medium heat and hold 2-4 inches from the stain. Buff the stain with the napkin or tee shirt as you heat the wood.

Not keen on tiles ... prefer a smooth surface with no grout lines to try and keep clean

Yes - they just needed help putting it all together :)

These chairs are easy to recover and the range of fabric available today gives you plenty of choice. I say go for it. If you don't feel up to it yourself get an upholsterer, but plenty of YouTube tutorials about.