Kristian Meller- your requirement for 'available as a whole series in a box' is kinda limiting, unfortunately, but I'll play along.
You can try out the
Gasaraki Complete Collection. Rightstuf has a special on it this week where you can get the ENTIRE series, 8 discs, for ~$35 USD. It's good for $35, but if you had to pay the MSRP of $110 I'm not sure I'd recommend it as highly. It's a mecha show with a LOT of drama type stuff thrown in. It's not great, but at $35 it's worth watching and owning.
Generator Gawl is another perfect collection I'd recommend. Personally I really enjoyed the show and if ADV does a remaster on it, for it's Anime Essential line, I'm going to pick it up again. It's a story of a couple of boys who travel back in time to keep the world from going in the negative direction it did and the one biy has an ability to turn into a monster, a Generator. The bad guys also have these Generators and they fight with Gawl and the rest on a regular basis. It's got some of the clumsy romance that people seem to enjoy and it was a damn good series IMO.
.hack//sign is getting the collection treatment. It's an Anime that takes place in The World. The World is an on-line game (not sure if you've seen this one or not, so I'll give you some info anyway). It's also based off of The World in the .hack games. Basically a boy is trapped playing in The World and cannot log out. The time he spends there (I say he, but well, I don't want to give anything more away...) he meets some friends and they all try to figure out why he can't log out, along with who the mysterious person Aura is. Pretty good, though I was just a little disappointed in the final episode.
Argentosoma is a pretty good watch as well. Seeing as how you liked EVA, and obviously like to think about Anime, I'd recommend you check this one out. It's been a while since I watched it, so I can't give you a proper description, sorry about that. I did like it when I watched it though, if that counts for anything.
I think someone already mentioned Crest/Banner of the Stars, both of which have or are getting collection treatment. I highly recommend this one to everyone.
I'd highly recommend
Bubblegum Crisis 2040 but the problem there is that I'd tell you to wait for it. ADV is giving it the Anime Essential treatment, and all the AE releases have been better than the originals.
You didn't mention it, but if you like comedies, you may want to check out
Excel Saga. Everyone seems to love this one, but personally I felt it wasn't as funny as ADV or anyone else would have you believe. It's got it's moments, but that's it. ADV tried to play it off as the funniest Anime ever... and it's not IMO.
Nadia collection 1 and
Collection 2 are GREAT. It's one of the best series I've seen in a long time. It's also animated by Gainax, the people who obviously did EVA.
Outlaw Star is freakin great too. I really enjoyed this one. If you like Bebop at all, you'd probably enjoy this one, though they are similar yet different.
Steel Angel Kurumi is another one of my favorite shows. It's got humor, some drama, action and fan service. It's a fast paced show, but highly enjoyable. After Vandread this is probably my most re-watched series, and it's pretty inexpensive in that box format.
Blue Gender has the romance, the action and the drama you seek as well. GREAT series IMO, and it's available in box format.
One series I think you'll enjoy that's not in a box format is
Full Metal Panic. It's got mecha, action and more clumsy romance. I also enjoyed this one a lot. I'm guessing ADV will stick it in a 'perfect collection' format at some point, but maybe not so soon, as it's pretty popular from what I can tell.
As far as whether you'd enjoy Bebop the series, it has more 'drama', more action and more humor than the movie. The movie was like a 90 minute episode. Take the amount of action found in the movie and squish it into 46 minutes (2 episodes worth) and that's what Bebop is like. I really enjoyed Bebop, but if you don't like the stand alone episode idea with only a 'not the focus of 90% of the show' bigger plot, then you wouldn't like this or Outlaw Star either IMO.
If you want further info on any of the series I recommended, let me know and I'll give you a bigger review/report on them. Let me know if you pick anything up from there.
Oh, if getting it to where you are is a problem, as long as you'd be willing to Pay Pal me the funds, I'd buy whatever you want and ship it to you, if that would help at all.
I also limited my recommendation to things that have, or are getting, a box set treament (well, except FMP!). There are plenty of other series I can recommend.
You can find these series cheaper elsewhere, I'm sure, I just ised Rightstuf for links because they are who I use exclusively for Anime.
I expect you and Benimaru may be the only ones to read through this entire post.