Okay, here's my 2p..
Headset - no real benefit changing it unless it's totally worn out (i.e bearing cups are worn out). They tend to last forever and replacement bearings are super cheap. Better to just change the bearings and regrease.. If you wanted a nore modern threadless version you would also have to switch forks and stem which leads to more £££
Bottom bracket - as headset. If it's a shimano sealed version and there's no grittiness or play in the bearings /axle movement it will go on and on.. Also in my experience some can be a real pain to remove
Single cog and chainrings - bit tricky this one. You could change the rings but when it comes to modern there's a chance you may need to buy a entire chainset. There's plenty of compatible ones floating about on the For Sale section here if you need some. Also if you plan to run a singlespeed cog, do you really need to run two chainrings up front? If so you will need a chain tensioner, or you could just use the rear mech as a makeshift..
Which leaves the wheels - I would personally invest what funds you have and stick to finding a lighter set. You could also get away with running 8 speeds using the thumbshifters you have which could be useful! They will not alter the looks of your bike too much and will make the ride quality way better than any of the parts above
Several bikes, one supportive lady and still trying not to buy anything else!