Need help with low-cost ideas on how to clean up, modernize, improve, etc. our 1950's bath. Just bought the house and completely renovated the kitchen so we really don't have a budget for this "bathroom" improvement.

What I like about the bathroom: the sink and toilet are relatively new (by Kohler) and the floor is simple white tiles... well that's about it!

What I don't like: the burgundy border. The grey tile isn't bad as far as 1950's bathroom tile goes but the border is unfortunate.

I don't believe we can remove the tile; we demo'd a tiled half bath off the kitchen and the tile was cemented to the wall, with wire mesh. We had to rent a demo hammer to chisel that off and nearly went deaf.

I have a few ideas but would love input, some fresh perspective or pros and cons of my thoughts.

Current ideas:
- glue beadboard over tile
- paint tile (not sure if this will be effective in the shower)
- use a grout removal tool to re-grout floor

Ideas? Thanks in advance!