Short version: start with the basics - maybe an amp emulator and a compressor. Learn how to use them really well, and then add other effects one or two at a time. You'll notice that there aren't many bass pedals in local stores, so I either a) buy online from a store with at least a 2 week return policy or b) buy something used that is very popular that I could easily resell without a loss.
Long version:
Individual pedals are probably (but not necessarily) going to cost more money overall. But to me it's worth it - I think there is more flexibility and better sounds available. I also like to sometimes tweak settings on pedals and it helps to just look at the knobs positions and turn them rather than digging through menus or remembering what the settings are on a digital pedal.
I don't have an amp, I always play direct. I started out with a SansAmp Programmable Bass Driver DI, which has an analog signal path, but the knob settings are still digital and you have 3 channels, which you may like. I liked the tone, but again I wanted to just look at the knobs and know how they're set so I recently picked up the new SansAmp VT Bass DI (I could have gotten the regular BDDI, but I wanted to try a different flavor).
The next most important effect to me is a compressor, which I leave always on. As mentioned by another post above, I started out with the MXR M87 for its LED indicators and noob friendliness. I used that for a couple years, but felt like I could hear it "pumping" so I recently replaced it with the Empress Compressor, which still has LED indicators and sounds more transparent to my ears.
I don't really use modulation, chorus, delay, etc. but I do like drive. Like others will tell you this is a very personal thing and everyone has their own preferences on "good tone." When I started out I thought I wanted a fuzz pedal, but I've either sold or returned all the ones I've bought (MXR M84, EHX Big Muff, JHS 4 Wheeler [Zvex Wooly Mammoth clone], and Empress). I think I've come to terms with the fact that I like OD and distortion, but not so much fuzz (unless the perfect one still eludes me out there somewhere). I have the Darkglass B3K for overdrive and I love that. Lately I've had GAS for a second OD or distortion to use in tandem with the B3K.