Vince should be able to give you a better answer than mine. The only mild cigar I can think of is the Nub CT 460---not sure of the retail on them but should be around $ 5, tho I have picked up some for $ 2 - $ 3. A good flavorful smoke that needs an hour or so to enjoy properly.
the 5 to 10 buck range is right in my wheel house. for starters the Vega fina Toro @5.25 is a great mild smoke , if you like maduro try the Bahia maduro, 9the Montecristo white corona about 9 bucks is mild as well as the romeo & julita reserve real ...... go to your local brick & morter shop & ask questions of the people working & see what they have in stock.... hope they can help ... Enjoy. Vince
I like trying new cigars by buying singles, or rather 2 or 3. 5 packs are good too, as if I don't like the first 2 or 3, I pass 2 on to my stepsons. The worst experience I had was buying 3 boxes of a cigar that I thought was pretty good. They didn't improve with age and it took 3 or 4 years to smoke them all (I wouldn't bet that 1 or more are still lost in a humidor). The only good thing about them was that they came in a beautiful box. You are more likely to find a cigar smoker without the same preferences as yourself as with.
Thought of another mild cigar you might like, Flor de Oliva and it's probably under $ 5.
Don't overlook the Macanudo and Don Diego brands; Don Diegos especially are both mild and inexpensive, while Macs are only slightly bolder and more expensive. Macanudos earned a reputation as "frat-boy cigars" because they are premium-quality cigars that first-time cigar smokers won't choke on.
I also like the 5 Vegas Gold. They're mild but very tasty, whereas the regular "red label" 5 Vegas line is more medium-bodied.
And when you're ready to buy in larger quantities, try a bundle of Casa de Garcia Connecticut (white label); I got a bundle before Christmas intending to let them age, but they were so good I ran out before the end of January.
(Please note: The Casa de Garcia brand is new to me, and their cigars may or may not already be aged past the "sick" period. My first shipment didn't last long enough to develop an ammonia taste; that happens with all cigars about three months after rolling and lasts around nine more months before they become smokeable again. The reason you almost never get any "sick" cigars is that all but the very cheapest ones are usually aged for a year or longer before they reach the retailers. CdGs cost between $20 and $30 per bundle of twenty, which is very cheap as handmade cigars go; hence the cautionary note.)
Any good tobacconist can always steer you to cigars that fit into your general flavor and strength preferences, once they know what they are; and most of them carry cigars in nearly all price ranges. Not every cigar they recommend may be just what you're looking for, but if you can discern the difference between strength and flavor you'll quickly learn why you enjoy the ones you like; then your tobacconist can be a lot more helpful.
tonygraz's idea of buying just two or three sticks is pretty sound. If you still can't decide about a particular cigar after your third one, it just doesn't turn you on enough to buy a larger quantity. (Right now, I mean. Your tastes will probably change some over time.)
I generally buy anything that's new-to-me as singles from a local shop, go back for two or three more if I like the first one enough, and then possibly graduate to five-packs from online vendors until I'm ready to buy an entire box/bundle. Then the local guy gets first crack at my business; he'll even special-order a brand/line/vitola he doesn't ordinarily sell, as long as I'm buying a whole box.
I've only tried one variety of RYJ's lineup and was not impressed. Nothing wrong with buying singles, but as has already been said, sometimes 2, 3 or more is a better idea for judging if the cigar is for you. I have often found inconsistency after smoking 5 of a particular cigar and that is somewhat of a turnoff about buying more. Nothing quite like buying a box of something and finding out that you really don't like them.