Very nice indeed! I have bnz 41 MP-40 2979f, but it's clearly seen much more use than yours has!
You'll probably want a phenolic (Bakelite) barrel resting bar to replace the one that's missing. Originals are nearly impossible to find since they were somewhat delicate and easily broken. A company called History Arms makes reproductions:
http://www.historyarms.com/rbar.html
They're nicely made. The only drawbacks are that they used an original NURAL aluminum resting bar for a pattern, which is slightly different in its dimensions from the Bakelite bar that originally equipped your gun. Also, the History Arms repro is not made of real Bakelite, but rather of some other slightly softer plastic that looks like it. This would be fine except that these cannot stand the heat of firing and will warp once your barrel gets hot. The solution is to buy one and notch it as in the photo below so that it is easy to install and remove when you go shooting. Just snap it in place with a finger tip. It's easy to pry off with a small flat blade screwdriver. Notching also means that you don't need to disturb the original retaining pin.
If you need a sling, PM me. I have an excellent condition MP38U40 marked original with the correct milled steel button that I'll sell you. I don't need two.
Advice that you never asked for: The magazines that will work best for your gun were made by Steyr and were marked 98E 40, 41, and 42. The code changed to kur in early 1942. These will fit and function perfectly every time. Other magazine makers had occasional serious quality control porblems. There are a couple of sellers in Eastern Eurpoe who consistantly have these. I was able to buy several recently from an unopened original crate of brand new 98E 41 mags in Poland. They're out there!
Steyr also made 98E & kur marked loaders, all with their WaA815 inspection stamp. These fit Steyr made mags perfectly.
Enjoy!