Just starting out, you might consider a classical acoustic with nylon strings. The strings have less tension so your fingers aren't deforming as much when you fret. The tone isn't as bright as a steel string acoustic. Some of the necks on these guitars are wider than steel strings, some are not. Why the difference I don't know.
There are plenty of great guitarists with cigar butt fingers.
Thank you, thank you, I'll be here all week.