14ga is fine for a 10A booster. In fact it's generally more than big enough for all considerations, if you're not doing O scale. But when you consider that #14 wire tends to be cheaply available at any big box store, such that saving money on a smaller gauge wire means more time shopping around than it's worth, that's really all the justification most people should need to use 14 gauge wire.
I disagree with peteski that we should base bus wire on short-circuit current, although it's true that you may have overload problems if you use too small a wire, and then combine that with poor soldering or relying on rail-joiners for electrical connectivity. The main reason we oversize our bus-wires is to avoid voltage drop, which noticeably effects our train speed. I think you are more likely to see ill-effects of voltage drop before your overload breaker stops working, although either one could be a warning of the other. But, see my first paragraph for why you can just use #14 and not worry.
I would say that solid vs stranded is a personal preference, and that one can make a direct analogy to preferring either 'easy-to-bend-smooth-curves' Atlas code 55 flextrack no 'holds-its-shape' Micro-Engineering.