Seeking advice: single speed conversion, Fuji ultimate road bike (old!) - Which kit? Which chain? etc First off - I'm a complete amateur when it comes to doing repairs on bikes. Anything exceeding changing tyres, tubes and perhaps adjusting the brakes is something I've never attempted before. However, I feel like I should get better at it, and this should be a great project. 

Here's a pic of my bike, a vintage (don't know precisely how old it is) Fuji Ultimate road bike (10-speed): 



I'd like to do the following things: 


Temove derailleurs, related cabling, gear shifters from bike
Replace the cassette with a single chain ring at the back, but not a fixed one. I'd like it to be single speed.
If possible, still use the cranks on the front (the small ring), without having to do any removal / replacement
Get a new chain and put it on
If possible: replace the current brake calipers with up-to-date (cheap-ish) ones, e.g. tektro brakes (but still leave the current brake levers on the bike)


I'd specifically like to ask you all for some advice regarding how to go about this project: 


Which parts will I need to buy, and what specifically would you recommend? I don't want to end up accidentally buying the wrong size ring/chain or something like that.
What tools will I need? I have a basic toolkit, and some pocket bike tools.
Are there some online tutorials you could point me towards? 
Will new (Tektro?) brakes fit on to this bike?
Will I manage this? :D


Finally, here is another picture of the rear wheel / hub / cassette of the bike, to provide slightly more information to everyone:
A bike this age will have a freewheel type hub (as opposed to a freehub). Sheldon Brows says a BMX freewheel can be used to replace the existing 5 speed freewheel. Hopefully the chainline would then align with your inner chainring, but you may have to re-space the rear hub and re-dish the wheel. 

See https://www.sheldonbrown.com/singlespeed.html

BTW the term cassette is generally only used to refer to the stack of sprockets used with a freehub, not a freewheel.

The tools you need will include a chainwhip and the appropriate freewheel removal tools. Park Tool Company has a good set of videos on freewheel removal and installation that includes identifying the appropriate tool. Link below.

I believe that BMX freewheels will come with a sprocket designed for a  1⁄8 in (3.2 mm) chain as also commonly used on single speed bikes, so that's the chain you'll want. You will need to look for a 1⁄8 in chainring that fits the crank spider. The existing rings will work fine with that chain - you'll want to check whichever ring you want to use for wear of course.

While we're talking about the cranks - your bottom bracket is likely to be worn out so you'll want to service and potentially replace that.

I can't see the dropouts in the pictures you included but you'll need a way to tension the chain properly. If the dropouts are slots that allow the wheel to be moved front to back you are good, otherwise you'll need an add on chain tensioner of some sort.

Park tool: