I never base what I'm going to promote my first city to on my first city, but on my second and third. My style is very unit-based, so a productive fortress is important to me (if you play with, say,  a single assassin hero, it wouldn't be important at all). Your first city is the only one you can guarantee will be good (assuming you have a 9-resource tile), but that doesn't mean you won't soon run across one that will be better...

As an example, you generally don't want multiple fortresses too early, and all else being equal 3-3-3 I find superior to 4-2-3 or 4-3-2. On the other hand, you don't want to put off establishing your Arsenal too long (it takes forever to get all the force multipliers in place, especially if you have access to some wonders) - don't let perfect be the enemy of good. So I would make my first site a fortress unless I'd already scouted (preferably, already settled) a tile that is better. You can probably make up your quota of towns from marginal sites as you expand, so if you have two wonderful tiles to start with, I'd think seriously about making the better one a fortress and the next a conclave (again, especially if you expect to have access to some wonders).

Thanks. This is very helpful to me.

For me, it depends on a lot of different factors.  I like first-city fortresses to use as pioneer pumps, but it also depends on the faction I'm playing.  If I'm playing a faction that's going to need a lot of mana, I might consider making it a conclave.  If I plan on building lots of units or playing a money-intensive faction like Altar, then I would strongly consider making this first city a town especially if it's near a river.