www.amazon.co.jp has site options to shop in english, and ships internationally (although only by UPS express). I ordered a bunch of manga in bulk once, and the price actually turned out to be pretty reasonable considering you're paying japanese cover price (usually about 450-550 yen ~= $5) per copy + an equal amount in shipping/customs; which basically puts it at the cover price for a fully translated volume at the bookstore. They will pretty much have hands down the largest selection you can find online.
www.yesasia.com has a slight premium on the cover price, but offers free shipping options on a lot of their products. Selection is a bit more limited, but they seem to have a lot of the popular titles.
As for recommendations, since you're still relying on a dictionary quite heavily, I'd recommend mostly shounen titles as they'll have the furigana beside all the kanji.
Black Cat is a definite recommend, D. grayman was good too, but I never got to finish it.
The Mai Hime manga was a semi-decent read from what I remember when I was working on it with a scanlating group. It follows a quite different storyline from the anime.
Oh, and for the love of god, read Gintama. Having a decent knowledge of other series and japanese puns is a plus. It's one of those series that can go from absolutely absurd to super serious without missing a beat.
Also, Berserk isn't technically finished, just on indefinite hiatus. The author took an extended leave of absence so he could play Xbox and browse video sites all day.