A "star base" would be a very large, engine-less warship transported via tugs, I guess.
As for its design, well, it could have both beam weapons and missile launchers, house small spacecraft and mount very powerful sensors. Though as far as static detection's concerned, I believe it's cheaper and more effective to just drop some deep space tracking stations on some random asteroid/moon.
However, I don't think it'd be particularly practical, since it would be huge and huge military vessels are specially expensive. You're better off having a mobile fleet. Besides, as a military ship, the star base would also suffer from maintenance decay, so that's yet another disadvantage. As far as static platforms are concerned, I prefer to use small-ish ones to defend jump points, but that's about it. PDCs are more economical for colony defense, I believe.