I'll throw in a few suggestions too.
If you're new to cigar smoking you shouldn't have too much trouble with any of the Hoyo de Monterrey Excaliburs. If I were you I'd try both the natural and maduro versions and see which you tend to prefer. A lot of folks like the odd numbered Excaliburs -- I, III, etc -- these are often touted as the best of the bunch. Starting off, the Excalibur I might be a bit daunting just by size alone. I remember when I started out the III in maduro pushed all the right buttons. Great balance of strength and flavor. Also from the Villazon factory are the tissue wrapped El Rey del Mundo Robusto series and Rectangulares. Good smokes, IMO. Along similar lines you might want to check out the Punch delux series or Punch/Hoyo de Monterrey regular line Robustos. But they tend to lack the same kind of finesse -- at least initially. Generally these are all around medium -- mendium full strength smokes.
I'd recommend the Padron Anniversarios either in natural or maduro, if you don't mind parting with the cash. It's been a long time for me with these but I remember them being smooth as silk with tons of flavor. I'd call these mild-medium.
If you're interested in Cameroon wrappers, I'd look into the Arturo Fuentes. Cammies have a nice savory spicyness to them that a lot of folks like. For some reason I get the impression that non-smokers tend to not mind the smell of a Fuente too much. Mild-medium again.
You might like Private Stock from the Domincan. These are nice creamy, smooth and relatively inexpensive. Mild-medium.
I'm a big fan of Torano products, so I'd be remiss without mentioning them. Try the Reserva Selectas in the glass tubes or the Brazilian wrapped Signatures. The Signatures are my favorite. Smooth with big flavor! For something with a little more power in the Torano lines look to the Exodus 1959 "Maduro". Reserva Selectas -- mild, Signatures -- medium, Exodus maduro -- med-full.
A lot of folks like Fonsecas. I tend not to like the products of that particular factory. Taste is subjective though and since they're not too expensive you might as well try them. Mild.
For more mild-med and flavorful suggestions I'll point you to Havana Sunrise and Honduran/Cameroon Embassy. They're also cheap. From a value standpoint I give these a high recommendation.
I'll second the suggestions for La Gloria Cubanas and Bahia Golds.
Cheers and good smokin' to ya.