Oliva is a good maker and Placensia is making some stuff that the aficionados are really into. Both makers offer sticks in the $10-$15 range.
Other than that, it's hard to recommend anything unless you know what someone likes. Are you into milder flavors or more robust? What kind of cutter do you have? You can't clip a figurado (rounded or pointed cap cigars) if you only have a punch and not a cutter. Also, on the topic of cutters, stay away from V cutters. Most of them are trash, and even the good ones can fuck up the cap if you don't know what you're doing. You really want a double bladed guillotine style cutter to start with.
Also, stay away from the jet torch style lighters. Look for a "soft flame" lighter instead. The jet flame style lighters can fuck up the taste of a cigar in the hands of a novice. The soft flame lighter is a similar flame to like a Bic lighter, but without the horrible taste.
The way you cut and light a cigar will have a noticable impact on the experience.
There's a lot that goes into it. The best thing you can do is find a good smoke shop, drop $50 on a few sticks the tobacconist recommends, and figure out what you're into. Grab a candela if one is available - they're wrapped in a green leaf and are usually pretty mild. I'm not even into mild cigars, but they are some of my favorite smokes.
@Unarmed-Dindu 3-4 cigars a week is basically harmless unless you're a faggot trying to inhale them. The only thing you really have to worry about is mouth cancer, but I'd only worry about that if I was smoking 2-3 cigars every day.
Oh yeah, get a humidor. That's essential if you don't want your cigars to crack and fall apart