I want to learn the styles best for self defense. So which would be a better grappling martial art for street defense, judo or bjj (or any other suggestions)? And as for striking, between karate, boxing, or kickboxing (once again, any others) what's the best bet?
First of all, I'd recommend you take a look at the
FAQ on finding a good martial arts school. In general, signs to look for are a competitive record, regular heavy contact sparring and 'aliveness' (if you're unfamiliar with the term, Matt Thornton has a
long article on the topic describing what it is and why it's important: he is the man most associated with popularising the concept).
If your interest is mainly in striking, the safest option if you want decent training is muay thai (which you'll also see as 'thai boxing'), along with martial arts like boxing and kyokushin karate. That's not to say there aren't good schools within other striking styles, but they tend to vary widely in quality.
If you're more interested in grappling, then BJJ would be an excellent choice, as the strong competitive element and ability-based ranking system generally results in high quality training. A cheaper option is judo, which is also much easier to find - the two styles are closely related, the main difference being that judo normally focuses on throws whereas BJJ is mostly about the ground. For more on judo, read the Bullshido.com
article - there is an article on
BJJ too (you could also check my
BJJ Beginner FAQ). SAMBO is another good choice, but even harder to find than BJJ. Then there's wrestling, which is also great training for grappling.
Alternately, you could combine grappling and striking by cross-training in several arts, or at an MMA gym (though technically 'MMA' is a ruleset rather than a specific style). Examples of well known MMA gyms would be
Team Quest and
Miletich Fighting Systems.
Finally, you could try having a look through the
dojo reviews section, which might yield something more specific to your area, or use the search function (the link is at the top right of the page).
There are also several school databases you could try. For example, for BJJ:
TrainJiuJitsu.comGym Database (BJJ, MMA etc)
UK Club Map