The following are notes and musings from my years of bass playing. They are really just observations based on experience of playing in two different sorts of environments, the church and the rock band. If they help anyone else, all well and good.
Someone once commented in a buyer's guide that bassists, unlike guitarists, seem to accept that you pay for what you get, and that budget prices mean budget guitars. Perhaps that was an unfair comment, but it is true that there is a wide range of prices for bass guitars, from £100-£200 for beginner's instruments to, well, the sky's the limit, but at least £1,500-£2,000 for a "name" bass like a Wal. Having said that, bassists are also less conservative than guitarists are, or at least were until recently, and more willing to experiment with lesser-known makes if they like the feel of a particular instrument, although such staple favourites as Fender Precision and Rickenbacker 4001 are still quite popular.
Budget bass guitars are nevertheless not awful. They may not be so pleasurable to play as a more expensive or better-known make, but as long as the pickups work and the neck is not bent, then you should be able to play bass with one. If the bass feels very awkward or stiff, try adjusting the action of the strings and fitting a lighter string set. I was amazed at how much more dexterous my fingers became when I did the latter. On more expensive models, active circuitry is nice but always remember to carry a spare battery, especially if your model won't work at all if the battery is flat (some basses have a passive/active switch that can cover such emergencies). A case is pretty essential - if you can't afford a solid one, at least get a so-called "gig bag", which is a non-rigid but fairly padded case.
A word is in order about what one might call "exotic" basses: five-, six- or eight-string instruments, or double-neck basses. The usefulness of these instruments varies as much according to the sort of music you want to play as their inherent design, although to be frank the amount of people using eight-string basses (four strings, each doubled up with an extra string an octave higher) or double-neck basses (two necks on one guitar, one a conventional bass and the other, well, really anything you want!) is fairly minimal. In addition these instruments pose limitations of their own, such as the possible need to use a plectrum instead of fingers (on the eight-string) or the extra weight of the instrument (the twin-neck). Five-string and six-string basses are more widely accepted, having caught on in the last twenty years or so, but still have not supplanted the traditional four-string, even among big name professionals. This is because not everyone wants to play notes lower than the usual E or hear high-sounding bass notes. On the other hand it is often advantageous to be able to dip lower than E occasionally, especially when following bass parts written for the keyboard, and having an extra string at the top can make large note stretches more practical. Offset against this is of course the extra weight (in some cases) and cost of the instrument. I personally think that for most players it is best to start out on the conventional four string.
When it comes to amplification, don't forget that a good amp makes a big difference to your sound. Having said that, if you are strapped for cash then sheer wattage may be more important than a good name. Conservatively you probably need 50 watts to play in a band, nearer 100 if you want to play with a loud drummer. The other point to remember (one that is sadly lost too often) is that the amount of wattage is not there to be yanked up to eleven all the time, but simply to provide you with a decent sound at lower volumes. For example, half-volume on a 100 watt amp often sounds better than full volume on a 50 watt amp. Desirable features on a subsequent amp, if not your first one, are an effects loop and a graphic equaliser, and inputs for both active and passive bass (these may also be "High" and "Low"). Castor wheels on large units may be nice if you are not a particularly strong person.
... are those accessories which are in fact fairly vital to playing. You need at least one jack lead to connect your guitar to the amp, more if you are using an effects unit or want to keep a tuner online while playing. The straight ones tend to last longer than the curly ones, which now seem to have fallen out of favour. If you want to play standing up (and virtually all bassists in bands do) then you will also need a strap. Bass guitar straps are normally rather wider than their guitar equivalents owing to the greater weight of the instrument. Finally, a bag to keep all your bits and pieces in (strap, leads, tuner, books, etc) is a good investment.
I cover these separately because they are not absolutely essential, and indeed some purists might question the very concept of bass effects. Some effects units come with a tuning function built in, but you can also buy tuners nowadays very cheaply, from mass electronic outlets as well as music shops. To be honest I think that tuners are worth their weight in gold, not because I am tone deaf (I can tell when a piano is going out of tune) but because they save a lot of time and hassle, in particular in situations where everyone else is making so much noise that you can't hear the differences between the harmonics that you ping on the strings in an effort to hear if you instrument is in tune. With a tuner you just plug the guitar in and adjust the machine heads (tuning pegs) until the fluctuating needle is steady in the middle of the dial. And let's be honest, an out-of-tune bass playing with other instruments sounds awful (though not nearly as bad as an out-of-tune violin).
Contrary to what some people think, effects were never the monopoly of guitarists: even in the sixties there was fuzz bass, although it was a bit of an acquired taste. Some bassists have made brilliantly successful careers for themselves without using these gadgets, and as I said, they are not essential to be a good bass player. In fact overuse of them can not only be irritating to the listener but can detract from the bass's main function, which is harmony and rhythm. To a large degree your chosen style of music will also dictate the usefulness or otherwise of effects. Nevertheless a bit of flange, chorus or octave divider can sound good in the right context. Bass guitar effects start from a few ten-pound notes for single-effect units, through around £100-£300 for integrated units at amateur or semi-pro standard, to however much you want to pay if you're a professional.
If you are serious about learning to play bass, sooner or later (usually sooner) you will have to face up to the need for one or both of the above. You can learn to play basslines by playing along with tracks on your stereo, but this takes a while to pick up and has the disadvantage that it is very hard to learn the principles of bass playing this way, especially if you want to do your own material.
Now that so many books come with CDs which play you the tracks that are transcribed on paper, one might think that the need for human tutors has declined. However this is not necessarily so: many people will always want a guiding hand, at least at first. A tutor can point out where you are going wrong and wean you off bad habits early on. A book of course has the advantage of always being there when you want to practise, and once you have bought it there is no further expenditure! Really you have to decide what's best for you. One thing I would recommend however is that you don't shy away from learning music theory, as this can be the key to playing the right notes whatever chord structures the band, group or orchestra throw at you.