I'm also voting for skipping BW1 if time and money is of concern. While there are story components that might not be overly clear if you haven't played the first game, they are partially summarised when the time arises and honestly, it's a Pokemon game - the story is largely irrelevant.
BW2, in my opinion, is what the first games should have been. The world is more interesting, the selection of Pokemon is vastly superior and the game feels decidedly better in every way. Now, while it has been improved and changed, a lot of things are shared between the games. For this reason, I worry that playing both in quick succession could be repetitive.
On the downside, some areas of BW2 aren't really fleshed out, because they are inherited from the first duo and not entirely relevant to the story. That said, there is enough new content to make up for that.
If you're looking for a more rewarding game, you can connect with a Black2 player who has beaten the Elite 4 and acquire "Challenge Mode", which pumps levels of opponents and makes the AI smarter. Gym Leaders and Elite 4 also get a minor lineup change.
I really want to stress the number of pokemon again, though. BW2's Unova dex (ie, before it gets expanded to the national Dex post-game) has 300 pokemon. BW1 had 155. This massive inclusion of pokemon made the game so much richer. There are constantly new and interesting pokemon in each area. It's not the caves=zubat/geodude/[wildcard] affair of the past. Almost every environment has a fresh roster of encounters.
If I could make one complaint, which goes for BW1 as well - why do 90% of the trainers in the game have 1-2 pokemon? Earlier on, I understand, but even most of Victory Road is full of trainers with 2 pokemon. You should be fighting 3 or 4, at least. Even the default Elite 4 have 4 pokemon each (Champ has 6).