The future of scanning in Ashtabula County is still somewhat unknown.
The County Sheriff's Department will be moving to MARCS soon, that's a fact (which means you'll need a digital scanner in order to listen). However, the towns of Geneva on the Lake, Andover, Orwell, and Jefferson are all in question. According to the Star-Beacon, they also need to upgrade to MARCS, or the County S.O. will stop providing them radio service at the end of the year.
http://www.starbeacon.com/archivesearch/local_story_283220756.html
I'll be interested to see what happens, since most of these towns can't really afford to make an upgrade.
So bottom line: If all you plan on monitoring is Geneva, then you should be fine with just about any scanner (same goes for Ashtabula City). I don't think either town has any plans for upgrading their radio system anytime soon.
But if you would also like to monitor Ohio's MARCS System (which also includes OSP), Lake County, and (soon to be) Geauga County, you'll need a digital trunking scanner.
Also keep in mind that Lake and Geauga Co's both simulcast, meaning that you'll hear Wickliffe PD just as clear as you'll hear Madison PD's (which I think is a big plus).
So, living in Geneva, I would strongly recommend a digital trunking scanner. You can listen to SO MUCH more than just the Geneva PD.