As noted above you need to cut the steerer tube to length - but I wouldn't do that just yet, you need the headset installed first as there is a good chance that you will cut it to the wrong length.
Your headset options are pretty straight forward - there doesn't appear to be a seat where the bearings sit in the frame so you need a headset that presses into the head tube and the bearings sit above and below. There are some differences between headsets with slightly more or less spacing below the head tube, this will make the headtube angle change slightly but it's unlikely to make a noticeable difference to they way the bike handles.
A couple of examples are the BBB BHP-01/02 which would work well, Cane Creek does one (40 Series) and may have better availability where you are. Again I wouldn't worry too much about performance differences so get whatever you can that will fit.
SJS Cycles Headsets
The stumbling block is fitting them - you'll need the crown race fitting which may or may not be straightforward - some are split which means they fit really easily some aren't and need specialty tools to press on, I've had a couple of bikes where I struggled to get it to fit and took it my local shop and they fitted it for me. One was a steel frame bike and the fork needed a little milling to get the crown race to fit and this is in the realm of specialty tools that cost a lot of money. The headset can then be fitted into the frame with a bearing press.
I've built a few bikes now and I generally get the headset fitted by my local shop, doesn't cost too much and having a good relationship with a good local bike shop will pay dividends in the long run.
Once you've got the headset fitted you can put the fork in and decide how much (if anything) you want to cut from the tube, I have a suspicion that once you've got the bearings fitted and a spacer and stem then there will be only be about 60mm or so of exposed steerer - you won't know how many spacers you want to keep until you've had a chance to ride the bike and see how well it fits you. Once you've settled on how it fits (it's always worth keeping an extra spacer above the stem anyway for flexibility) then you can cut the stem to fit, but it's the very last thing you should do.
Edit to add: Those drawings are great, really helped figure out what you needed!
