You definitely want to keep Ulster, it is rich and taking out the Irish is either priority 1 or 2 for the Scots (Picts being the other). The province with the rebels on the mainland (Reget?) isn't worth it in the early game, that's a tough fight and I think the province has a high unrest factor. It spawns some nasty troops.

The Scots are tough, Clansmen are nice, but unreliable. You will want to build up clansmen in Ulster to hold the province, and start building Clansmen in Sci as well, since they get a valour bonus there. Build the shrines/chapels in Sci and Ulster to boost morale for troops built there. Have another province work on getting spearmen, you will need spears as an anchor, while you flank with Clansmen. I usually try to tech up to ships in Dal Riada, to support Ulster from the mainland and guard against Viking raids.

One other trick, on turn 1 destroy your Abbeys. You will get 1000 bucks in cash, and it will keep the Vikings off of you. If you leave them, they will attack and you will lose them anyway, along with a lot of troops.