Bathroom Touch-up (including retiling shower base)

Me and my wife just bought a new apartment.... (yay!)

The bathroom is very shabby - but at this stage we cannot afford a complete professional reno (which is the ideal solution). That is a couple of years away. In the mean time -

We would like to touch up the bathroom, and I have the following ideas:

- White Knight tile paint on the wall tiles, surrounding the bath and also the wall tiles in the shower recess. ($100?)

- A new cheap vanity picked up on auction. ($150)

- Paint entire Bathroom. ($100)

- New mirror on wall. ($200)

(Potentially new taps - $300)

But would like some assistance:

I cannot place white knight paint on the floor tiles - I have previously done tiling as a handyman at my last job, but am not certain about waterproofing.

The biggest problem I have is retiling the shower base - I am worried if I pull the old tiles I will damage the waterproofing and cause a leak (potentially into the apartment below)

I am worried if I tile over the shower base the tiles will not stick well, also defeating the purpose.

The same applies to the bathroom floor but due to the height difference I am not willling to tile over. If it will be too hard to pull the tiles and rewaterproof I will just give this a miss.

Any tips?