Right now, we have different things we can try to steal. Those are either the already-developed technologies from last turn (where we know which ones there are) or the ones developed this turn (where we have to guess). In total, those are:
Paddle Wheel Boat [Expensive]
Steam Engine [Expensive]
Rifling [Expensive]
Samara Rifled Musket
Gravity-Fed Magazine [Expensive]
Compressed Air Reservoir [Expensive]
Paddle and Ratchet [Expensive]
Victoria Air Rifle
Baby Bess Carbine
Lord Locke Pistol
Jaegar Cutter
Of the basic tech, Rifling and the Steam engine are the most interesting ones, I think. We can develop the paddle wheel boat ourselves later (with more experience than they have in both ships and - then - steam technology). Gravity-fed magazines and paddle-and-ratchet are of use with breechloaders (so much later) while air rifles are going to be a dead end.
Now, for the other parties. I think we can be pretty sure that Dunwich will be developing artillery both against Ft. Combe and Ft. Alton's horse riders. The only interesting question is whether they will opt for a more conservative design (where stealing will not help us much) or a more outlandish design (Like an Armstrong-seal breech-loading rifled cannon, which will not work well for them but give us quite a few things to steal).
In the end, I'll vote for either stealing the Steam engine, or Dunwich's revision.
Normally, I am against stealing the Atterton Monarchy's designs, mostly because I have a fairly low opinion on their final designs as going for the shiny instead of proven tech, but that might actually be what we'd need this turn - many technological ideas we can use the best of later.
@Zanzetkuken: Can we steal basic tech (i.e. Rifling, Paddle and Ratchet etc)?