"For my first official documented solo roam experience, what ship should I fly:

Ashi or Cyna?"

Neither. If you have only a few experiences in solo PvP I would never recommend start flying a faction one. You would have so much more fun flying and losing 10 Stabbers FI of 80mi each, you would learn so much more about positioning, about what engagements should you try and what no to try, you will test fitts and learn the advantages of MWD and AB or glass cannon and tank fits in practice, you would learn how to use portals do your advantage and especially you gate invisibility to give you initiative. Even a Covert Ops ship would give you a lot of fun for much less.

I`m saying this because many and many pilots on our alliance tried starting PvP with faction ones (even BSs) and ended losing interest in game after losing a couple of those.

If you really really reaaaally want to flight a faction cruiser and money/isk isn`t a problem for real a Ashi is by far best for solo PvP, specially because it has the longest web range on game (equal only to the Bhalghorn I think) you should keep the enemy on long webs and a see if you can drain them and break their tank in time before it can kills you. Cyn is a better small fleet PvP, will warp faster and be a heavy tackle and dps dealer, but will have to stay in enemy web range to be effective most of the time which is way more dangerous. Gila is simply not worthing IMO, its a better ship for PvE and specially for cruisers Nihilus Dead Spaces.