There's no order you NEED to get them in. In terms of installation, the games will work no matter which order you install them in just as long as you install the original sims 2 game first.
As for fun order of games to buy them in for fun reasons, I'd say you have a good order, because nightlife allows cars, (and you said you want to get that first) So say you want to build a business, and you didn't have nightlife, then you'd have to call a taxi every time you wanted to go to your business, so I think it's a good idea to get nightlife before open for business. But again, there's no important reason to get one expansion specifically before the next one.
As for differences, I'll only describe the ones you mentioned, but here's a link to look at all of the different expansion/stuff packs to see what they come with:
(just click on learn more beside which game you want more information about)
But as for the installations you mentioned:
Nightlife comes with cars, which is awesome, and my favorite feature. But there are other cool things about this expansion. It comes with the ability to date other sims, have group outings with your friends, and comes with the new location "downtown". There's lots of new things to do like go bowling, and hire a matchmaker. You can also become a vampire in this game.
Open for Business:
Pretty much you can only open businesses with this one. It's still really fun though, and I'd have to say it's my personal favorite expansion. You can open pretty much any business you want. And you can now learn skills.
You can now get pets... pretty much just cats or dogs, although you can also get a bird or guinea pig too, but they don't really count. You can also train your pet and it can have a job if you need some help with the family funds.
hope you have fun playing the sims :D