Recently bought a frame and forks to start a bike project, headset seems to be missing a part. It would be great if you could tell me what part it is that I am missing and also where I could purchase this part. It seems to me like it is some sort of cap that needs to be put in place over the existing headset.

You are missing the bearing balls or cartridge, the top race and the centering cone. Frankly, I recommend going to a bike shop and starting with a brand new complete headset.

This reminds me of when my mother used to tell me that I'd lose my head if it wasn't attached.

Youseem to be missing everything that isn't pressed onto (into) the fork or frame. Unless there's a bunch of parts; balls, top bearing race, centering cone, etc. that aren't in the photo, you need a new headset.

So,if I purchase a cup removal tool will that completely come off and will I be able to install an entirely new headset?

A cup removal tool will d 2/3rds of the job. You also have to remove the crown race form the fork.

Removing a crown race can be simple or difficult depending on the shape of the bottom of the race and the size of the crown. If the race overhangs the fork it's easy to set a punch behind it and start working it up. Keep it straight and it'll come off clean. However many crowns these days are larger than the races, which can make getting the race started difficult.

As for a cup removal tool. If you're not going to do this job often you might want to save the $30 or so cost of the tool. Here's how you can make one for much less. You'll need to find a coin (or disc) with a diameter just a bit smaller than the headtube's ID. File or grind two flats on opposide sides (racetrack shape when finished) so it'll slide up into the cup. Now push it behind the cup and let it flop flat, and use any punch to drive the cup out. Total cost whatever the value of the coin was plus a few minutes of your time.

Cool trick with the coin, FB, but I gotta say, my cup-remover-jawn (rt-1) has made me very popular at the coffee shop.
If that coin-trick gets out, my social life will be ruined.

Thanks All!
Removed the crown race from the fork and about to use that coin trick to take off cups. I'll update you when I'm finished. Off to find a suitable coin!

Do I need a threaded or a threadless headset?

You seem to missing the entire bike except for the fork and crown race

First time, cut me some slack

Ihope you'e kidding.

Is the fork threaded or not?

Threaded headests require a fork about 35-45, longer than the headtube (depends on the headset and amount of spacers used) with threads on the top 1" or so.

Threadless headsets require a fork 3" longer than the head tube, and as the name implies, without threads.

Perhaps it's not yet time to be building a bike up from the frame if you can't identify parts of a headset nor the difference between threaded and threadless fork/headset. For an inexperienced person in particular a build from scratch is probably the worst use of time and money for the return - either in finished product or in useful knowledge.