Start cheap (by your definition) on here, join the N00B PIB and sooner or later sign up for a vet. Pay no attention to suggestions to search "Thonginator". Really. You've been warned.
Really cheap no matter who you are-like 5ers for $3 cheap probably aren't worth it unless you really want to try sawdust or newspapery cigars. AMHIK. When even the copywriters here say a cigar is bad (Gerant's Golden Siesta, anyone?) its bad.
But imho there are plenty of good $10 or less 5ers for a newb, and some may become your "go-to" knock-about cigar when you don't want to worry about too nice a cigar or price tag.
That said, I've gotten to the point some of these vets are insinuating-I've sorted out my likes/dislikes and know why some cigars are inexpensive, some are mid-priced and yes, some are $15 and up. Also find the sizes you like-some guys are into Nubs and big azz ring gauges and others won't go above about 50 in trades or purchases. Learn to smoke more slowly-especially as a former cigarette smoker. This is a hobby, not a contest, and much cheaper than therapy!
I'd say try a few samplers too. I'm partial to LEC, Mark Twain, MoW and a few other lower priced ones. LHC Core, Oliva V, and Alec Bradley are what I'm "moving up to" and of course, Padron and Fuente....