Ok so, i hit VA a few months ago, promptly got bored, and quit for a while. I came back for S4, and was interested enough to start playing again. But I digress. I saw those cool antiproton weapons, and decided to acquire one, but realized that you need Marks of Honor. A quick trip to STO Wiki told me they could be found in the "Restoring the Neutral Zone" Daily mission. But upon checking the mission in game, it says I only receive emblems for completing this mission. What do you do to receive the Marks of Honor?
Short answer: you can't get Marks of Honor at VA from missions. BUT you can now convert emblems to Marks of Honor (or Valor, or Exploration) at Battle Group Omega. If you're a Fed, go to Nebula class ship USS T'Kumbra. For more info, see this.
You can go to Deep Space K-7 and find out, or browse the list of weapons and equipment. Most people wanted to get the Covariant Shield Array Mk X [Cap]x3, but with the Borg set, Aegis set, and Reman covariant, and Season 4 reducing capacity of covariants from 125% to 110% it's seemed to lose a lot of favor.