Assuming you have the money you'll need, the shortest route through systems (without requiring you to find a lot of obscure jumpholes) is:
New York -> Texas -> Bering / Hudson -> Hamburg -> New Berlin -> Stuttgart -> Omega 11 -> Omega 41 -> Omicron Theta

If you need to build up enough money to buy it first, then I suggest going to Bretonia. You should be able to barely scrape through missions there until you can buy a Bretonian fighter. Then, move on to Kusari or, if you're really confident, really good, and really lucky, Rheinland. Do the same as in Bretonia until you have a decent fighter, then make a run for Freeport 9 in Omicron Theta. If you're coming from Kusari space, there's a shorter way, which is:
Whatever Kusari System you're in -> Honshu -> Sigma 19 -> Sigma 17 -> Omicron Theta