I had a peek at IKEA's american website and it looks like the bathroomsection is lacking a bit compared to ours, and I know from experience (my brother lives in TX) Americans like their bathrooms more roomy and with more counterspace than whats common here.
That being said, with your preferred colors and style, it shouldn't be to hard to find something that won't fade in style and value the coming years.
For the vanity and other furniture there's a color called brown-black that's quite popular at the moment, you can get that in both the Hemnes, which is a traditional style comparable to the one in the picture, and Godmorgon which is a more "modern" style. If you want a more neutral color there's always high-gloss white and grey, which is also quite popular. One of the things IKEA is lacking is good selection of countertops and sinks for the bathroom, they're all basically all white sinks, and there's usually quite limited counterspace. But if you get a mirrorcabinet (fucking smart), you might not need it. Also, theres always the option of combining with kitchen/other furniture - e.g. most laminate or stone countertops is fine to use in the bathroom as long as you're aware of sealing all gaps with silicone etc.
Now, no matter where you buy your shit, get a good grip on what you want, and what you
needbefore choosing anything. I've had a lot of customers come in, decide on the fly and walk out with mediocre solutions.
Find out how much wall space you have on the wall where the vanity goes, that should be number one. Imo., 80 cm 2'6, should be a minimum.. Then see if you need any other cabinets, some people can easily cope with just the vanity. A highcabinet or two (or more) is nice for towels and more bulky stuff and you can use those both on the same wall as the vanity or separately, you can get those with mirrordoor too, if you want a fullfigure mirror in the bathroom. Lastly decide if you need stuff like a mirrorcabinet over the sink or other shallow wallcabs, and solitary shelves or movable knickknacks. Certain things you want hidden, but some stuff can just as well sit in an open storage rack.
Also, switching taps and/or sink isn't to complicated, so in a few years if you're not happy with it, or you wanna change something before selling, it's totally doable, and shouldn't cost that much. The usually most expensive things when renovating bathroom is tiles, bath/shower and the work. I guess you have pretty strict regulations on what you can do yourself, but never underestimate doing the shit you're allowed to do
Sorry about the long post, got a bit carried away, I guess 8 hours a day don't tire me out on this shit.
Example of HEMNES: