Obviously my attention to detail is lacking as I didnt note the last two questions...
iamjosh summed it up pretty well...what do you like the look of regarding live rock? I suggest looking at several types at LFS's and seeing what it is that you like or dont like then go get some! The different types vary from region to region. I didnt choose Fiji cuase it seems like everyone has that in their tanks and I wanted something a little different. I chose Kaelini as it had just hit the market, was nicely shaped, and had excellent coralline algae colors and was heavily coated on the rock. Recently I have seen some great shaped Tonga/Eva that appears as a fused conglomeration of Tonga Branches and just blew me away with the coralline algae coverage, color and tons of life that had survived shipment. In fact I would have bought a couple of hundred pounds if they had had that much in stock! I will do so the next time I am in San Francisco and they have some that nice again!!! But these two types of Live Rock are just my personal preference and in no way am I implying that its better than any other types out there. Again, check various types out and choose what fits your taste.
As far as base rock and live rock I am not exactly sure what you mean. Some live rock is sold as base rock and its usually mediocre shapped pieces best used as a foundation for your more choice live rock pieces to be stacked on. As such it is usually cheaper. However a very common practice is to use dry calcium based rock such as a rock refered to as "Lace Rock" to be used as base rock for your more nicer shaped pieces of live rock. This "Lace Rock" can be had in some very nice shapes, used as ledges and what not and will quickly be colonized buy bacteria and become live as will as become coralline algae covered. It is usually considerably cheaper than live rock and is often used by those on a really tight budget or those with HUGE tanks that require a lot of rock and its too prohibitively expensive to completely do in Live Rock.
I hope the above information adequately answered your concerns and questions.