If you can afford it, I'd first buy a cheap multi effects pedal. My first pedal was a Digitech BP80. Think of it like the starter packs you may have started playing bass on. Sure, the amp and bass were mediocre, and you would never gig with them, and upgrading either made your tone 5x better, but it gave you a feel for the instrument and helped you figure out where to go from there gear wise. While I can't speak for the quality of other multi effects, the thing about them is that they always sound great until you actually own the effect they're trying to emulate. NEVER gig with one under $500. And I wouldn't even recommend one then because you lose a lot of flexibility with each individual effect.
After that, as others have said, go for a dirt pedal. This depends a lot on the player and genre.
http://bassfuzz.com/ is a good place to start for this, but here's some of my suggestions:
Catalinbread SFT- fantastic low- or medium-gain overdrive, which definitely lives up to the hype. The thing about Catalinbread is that they offer the best of both worlds between boutique and large pedal makers. They are boutique quality, all the pedals are handmade in the US, and you know that your money is going to a smaller company. But, at $160, they rival the big companies in terms of price. Plus, their pedals are all very professional looking. They also have great customer service, and a TB account.
Music ElectroniX Messdrive Hybrid Plus- Jack of all trades sort of pedal. Most of what I said about the SFT applies here as well. While I don't own any of their pedals, I have dealt with the company before, and Os answered my questions promptly and politely. Review on bassfuzz, along with a number of other Electronix pedals, BTW
Tech21 VTBass- Similar to the SFT. No personal experience, but receives a lot of love on this board.
ElectroHarmonix Bass Big Muff- It's as versatile as it is cheap. The tone is decent as well. Muff are all very high gain, BTW, so if you don't want anything too extreme, stay away.
As for the second pedal, there is no "standard" for what it should be. It's really a matter of personal choice. But for most, it's some kind of modulation (chorus, phaser, flanger, etc), a wah, or an envelope filter. I've never heard of it being an octaver, but that doesn't mean you shouldn't. If you want an octaver, I can't give you much help from first hand experience, as I'm looking into getting one myself. But here's some suggestions:
MXR Bass Octave Deluxe and Aguilar Octamizer- Like the VTBass and the SFT, similar pedals which both receive lots of love here. both are fantastic, and are some of the best tracking analog octavers around
EHX POG (and its varients)- I don't like these much, but they're worth mentioning. They're digital, so they sound too harsh for some people (myself included) but the tracking is fantastic (although both the BOD and the Octamizer come close). I'd only get them if you need octave up as well as down. Also, they cost quite a bit more the the other 2, other than the Micro POG.