Search the archives for this one, there has been a lot of talk on this. Most people prefer direct. But try both you never know. Also I like to send a line direct and and one to a cab which I use a beta 52 to mic then mix the signals. Any mic that is good on the kick will probably work for bass as well. AKG d112 is a good example as well.
Which amp depends on which tone you want so its up to you. If you are recording into digital and have access to software EQs and Comps use them instead of recording with them to disk, this approach is way more flexible.
Maybe use a little bit of comp on the way in, especially if the bass player uses fingerpicking, to give you a more even recording.