When I started out I smoked the Portofino's a lot -- I did not have a humidor and they came in aluminum tubes that kept my cigars in good shape while I was golfing...
You might try the Arturo Fuente Hemingway series. From shortest to longest they are the Short Story (4x48), Best Seller (4.5x43), Signature (6x47), Classic (7x48), and the Masterpeice (9x52). They also have a "Barber Pole" called Between The Lines (4.25x46) which I have not yet tried. I prefer the Maduro wrapper but the Natural is good too. These are a mild-to-medium cigar that is very well constructed.
If you want something with a little more body I would check out Padron (again, I like the Maduro but Natural is good too). For a shorter smoke give the 2000 a try; the 4000 is a nice long smoking cigar.
If you want a very nice cigar higher-end cigar try any of the 1964 Anniversario (Exlcusivo - 5.5x50, Imperial - 6x54, Monarca - 6.5x46, or Principe - 4.5x46), Serie 1926 (#6 - 4.75x50, #9 - 5.25x56, 80 Years - 6.75x54 Perfecto), or Family Reserve (45 Years - 6x52) series of cigars a try.
Or, just start buying sampler packs from the various online retailers to get a broad variety of cigars to try.
