So I've not played with Pontus but here's an idea of how I might go about the opening part of the game. if Galatia rise to be the dominant power then you should take them out asap. You can maybe attack Sinope straight away and take it with Mercenaries and your starting stack. Trapesoz is another option, both would be ideal but I'd need to play the start to get a proper feel for who's around you. Then you can disband the mercenaries and hire some levies. Send your spy to have a look at where Galatia's armies are. If they are laying siege to Bythina (Nicomedia) then you could declare war and take Ancyra from them. This would give you a walled settlement that you could garrison if they sent there armies back to get you. You could even go and destroy their armies while they are laying siege to one of your neighbours. Another option is wait until they take Bithiyna and attack it as soon as they do. They wont have time to build up a garrison and their assaulting army will have taken losses in the siege. This will give you Nicomedia and take out one of their armies. You can then invade them using your spy to see where their other armies are. Best trying to fight them when they are weak or busy and if they are attacking other factions like Peragmon and bithiynia then you will build relations with them also. Try to build and keep momentum too. If you decide to consolidate when you cant even afford one stack then you are going to have a hard time defending yourself as your neighbours get stronger. The start of my campaign's are almost always about blitzing!
Ptolemaios Soter made a great guide a couple of posts down from this. I would not worry about it too much for the early game though. I would aim for a level 2 barracks in Amenisa but i would not wait for it to be finished before I went off conquering stuff. Things like population growth, infrastructure and research are things that should happen in the background while you are out expanding your lands. If you take Sinope you can maybe build a fish port there for food. For walled cities i usually just build from the yellow chain. Tavern for food, Theatre chain and slave trader. Temples, Barracks etc all go in minor towns. Apart from getting to build level 2 Barracks and the reforms I spend most of the first 100 turns researching the various civil techs and not military. Once you have a few provinces and you can breathe a bit more have a look at his post.
HTML Code:
https://www.twcenter.net/forums/showthread.php?800656-Province-Management-amp-Economy-Guide
As I say build a barracks but don't wait for it before going on the attack. Not sure about Pontus's roster but Guessing you can get some pike or hoplite units(I prefer pikes). Get 5-6 of these with 4 archers, 3-4 cav +cav general then the rest as Swords, Axes, peltasts, light spears or whatever you can get your hands on. Use the pikes to form a battle line with the archers behind and use your other units and cav to win the flanks