Need advice on my Pontos Campaign

It's 270 BC and I took Sinope, Ancyra, and Trapezous before disbanding the starting troops.

What types of gov or buildings should I construct first? Mines maybe?
And when will the "Big grey" break alliance and attack me?

Thx in advance

Before your ready for them too.

In Sinope and Trapezous construct a level one government. You may not be able to recruit anything from your Factional MIC until it reaches level three but once it does you will get all the best troops your faction can produce.
In Ancyra put a level four government and start turning out Celtic slingers. They'll keep the place safe for a while.
The AS will betray you within the next ten years, so don't expect the peace to last for long. The best advice to a Pontic player can give you is to use your starting stack to take Mazaka. It's a homeland province and far easier to defend than Amaseia, thanks to it's river crossings. Also if you attack the Seleukids instead of the other way around you get to keep all your alliances. Unlike the scenario where they attack you when you will loose them.
Concentrate on kicking them out of Asia Minor.
Whatever you do make sure to kick them out of Ipsos and Sardis. Otherwise you will be facing angry Seleukid stacks coming from both directions. Both provinces are wealthy so if you can keep a hold of them they will turn in a hefty profit with some mining upgrades.
Also bear in mind Hellenic Scythed Chariots are fairly cheap and although useless in a melee, you can use them to disrupt enemy formations like phalanxes. Followed by a cavalry charge or a shock infantry charge you can break even enemy elites.

damn, my starting stack is depleted and is disbanded so I'll have to scrap new ones to take Mazaka...

And when is the best time to build mines?

Well, when you can easily afford the 14000 mnai to build them and there isn't anything else very important like roads to be built. As Pontos, it might take you at least a decade before you can build mines.

I would recommend a level 3 in Sinope, for hoplites and peltastai to provide a supple but heavy support arm to your phalanx core. Pontos really doesn't have real elites yet(that's what I hear), but it has a wonderful variety of troops and that is your greatest strength, IMO. Be sure to make use of lighter troops as well.

Your biggest problem down the line is obvious....Big Grey. What you need to worry most about with that are your cities. You absolutely need to fight well and strike at your leisure if at all possible, because otherwise you get bogged-down and the population just gets sucked right out of your cities and you reach the point where you just cannot resist them any longer. That realization is very depressing and has tended to come for me around 230 or so. The key is in getting them out of Anatolia. If you can manage that, you should be strong enough to push into their heartland. Try enslaving towns you capture...your core cities need every little growth bonus they can get....

You probably wont have time to build an economy before the selucids attack you. What I did was pillage up a treasury then used that to build up an army of galatian mercs and eastern slingers which I used to kick the selucids off the coast and firmly establish myself from there.

I just started my first Pontos campaign, and I made the mistake of spreading eastward, taking Nikaea and Byzantion after initially capturing the obvious Sinope. Only through using phalangites in the east, and both abundant family member bodyguards and Galatian naked warriors in the west have I stayed intact. It seems that just a couple seasons after you get a positive income, the Seleucids attack.