How I changed my bathroom sink waste: with plenty of brute force and quite a lot of ignorance

The sink in the bathroom has a click-clack waste. One of those ones where you push it down and it clicks shut (plughole is plugged), and then you push it down again and it pops back up. My dad had previously complained that it was a bit sticky, as in it didn't always want to pop down or up. I basically ignored it - I don't ever need the sink to be plugged, therefore I have better things to do.

One night recently I noticed that the hot water out of the kitchen tap was cloudy. I poured a jug and looked at it and yep, it just had lots of bubbles in it. In my paranoia though, I thought about all the floorboards I'd lifted and replaced recently - what if I had stuck a screw through a pipe??? (very unlikely) Just to be sure, I thought I'd run some hot water in the bathroom sink upstairs. At least I could see if it was just the kitchen tap being weird. (I didn't really have a plan, I'll be honest.) So, I pressed the plug down, filled the sink, went 'uh huh' in a knowledgeable way at the water, and then tried to pop the plug back up.

The plug had picked 9.30pm on a Friday night the perfect time to make its transition from 'sticky' to 'stuck'.

I only have one bathroom.

The next morning, I discovered that my plug is extremely effective as a plug. Using a stray guinea pig hair as a reference, I could tell that absolutely no water had flowed away overnight.

OK, step one. Let's buy a new thingy. Two minutes later I'm googling slotted vs unslotted, what is the diameter of a sink waste...

• First things first, the thingy is called a waste.
• A slotted waste is for if you have an overflow hole in your sink. An unslotted waste is if you don't have an overflow hole. That's rarer.
• Plugs are all the same size underneath the sink.
• There's a couple of different styles of bathroom waste - the old fashioned one with a rubber bung/plug and chain, a click-clack/spring, flip-top/rotative and also freeflow. The bung ones are the cheapest. A freeflow one never actually fully blocks the sink - useful in, say, a downstairs loo, or in a public space, but not normally what you want.
• I opted for a flip-top. A plug and chain one needs cleaning and the chain gets in the way. A click-clack one has too many moving parts to go wrong. I'm not a council so I don't want a freeflow. Flip-top looks like the best option.