Yes, it's fine. Any camera can be a fine starting place, but I think it's nice to start one with relatively advanced controls (see Are there disadvantages to a prosumer camera for a beginner, aside from cost?). The X100 isn't terribly complicated, but it hits the important thing right on the head: direct access to individual dials for aperture and shutter speed.

One point to consider is whether the wide angle fixed focal length lens is flexible enough. There's plenty of controversy over whether beginners are better served by sticking to prime lenses like this or should start with the flexibility of zoom. Me, I'm on the "prime" side, but this really varies from person to person.

Of particular concern here, though: you'll be basically limited to a single angle of view — a "wide-normal". That's not necessarily bad, but it's kind of like learning to bicycle on a fixie. You're basically committing to a one lens, one camera, one year project. Limiting your choice intentionally can help you learn to really, really understand other aspects. And you'll learn to naturally understand the field of view of your lens without having the camera to your eye, which can be a really powerful way to find and make photographs.

That can be a powerful approach, but you also might find it limiting. Particularly, wider angles require you to be close to your subject to fill the frame, which is generally considered not ideal for portraiture (see Which focal-length lens is usually used for portrait photography, and why?) — and definitely forget getting details from a distance. But, you say you're primarily interested in street photography, and for that, this field of view is traditionally the thing (see What is a good focal length for street photography?).

You may consider Fujifilm's teleconversion lens or wide-conversion lens to help compensate, but honestly, I wouldn't really advise that — instead, if you feel you're not ready to commit to one focal length, I'd suggest getting one of Fujifilm interchangeable lens cameras — you should be able to find a used X-E1 for less than the X100 — or you could spring for the newer X-E2 or X-E2S, or even the X-T10, if you can push your budget (this is particularly important for improvements in autofocus, which are nice to have but not essential). But I'd suggest going cheaper, and springing for the beautiful 23mm f/1.4 if you can. That might be out of your pricepoint (looks to be around $650 used; $900 new), so the 35mm f/2 could be a good fallback ($400 new; not really worth the minimal savings from buying used currently). For either lens, remember that the lens can last many, many years and through many camera bodies, so you can mentally amortize it over many more years than you might the X100. (There's a rumor of cheaper, smaller 23mm f/2 in the works, but I definitely wouldn't suggest waiting when you could be out shooting now.)