If you're starting BJJ for the first time, then you will need to buy a gi. Some clubs, such as Gracie Barra, require people to buy their own branded gis, but others allow people to pick any gi they want.
If you've been looking for gis on eBay you may have noticed that some gis are labeled as judo gis, while others are labeled as BJJ gis.
There are a few differences between judo gis and BJJ gis. Firstly, judo gis tend to have baggier sleeves, and a longer skirt. In terms of the weight of the material and the thickness of the collar, a cheap 'student' judo gi is probably going to be very similar to a BJJ gi.
More expensive competition judo gis, however, are much heavier, and have a much thicker and harder collar.
BJJ gis, in contrast, have tighter cuffs both on the jacket and the pants, and a skirt that comes down only as far as the crest of the buttocks (in training, many people wear gis that are even shorter than this, but that would not be legal in competition). BJJ collars tend to be lighter and more flexible.
For day to day training, the weight of the material doesn't matter too much. Many people wear very lightweight 'travel gis' in the summer, and then 950gsm gis such as the Tatami Tank in the winter.
A heavy judo gi is closer to the 'tank' end of the spectrum. These gis may be very hot to wear, but other than that you shouldn't notice too much difference.
The cut does matter, however. If you like to do ezekiel chokes, then baggy sleeves are quite useful. If you like to perform the 'garotte' choke with your own lapel, then having a long lapel is handy.
In contrast, if you hate it when your sparring partners play worm guard, having a shorter lapel might be advantageous to you because it makes the gi harder to grab.
In competition, both the cut and weight of the gi matter a lot. A judo gi will be legal in a BJJ tournament that follows IBJJF rules, assuming it is the correct size. You would not be allowed to wear a BJJ gi at a judo tournament that uses IJF rules.
Most people would not choose to wear a judo gi for a BJJ tournament, even though it is legal, because judo gis are too heavy. While there are some rulesets that allow people to weigh in without their gi, the IBJJF and many other major promotions expect people to weigh in just before stepping on the mat, while wearing their uniform.
An average "competition legal" BJJ gi weighs less than 2kg. Judo gis can be double that in weight because the weave is so much thicker.
Judo gis are usually white or blue. BJJ gis used for competition are white, blue or black. There are also numerous other patterned and brightly colored gis available for BJJ that would be considered unacceptable at a judo tournament or even at a judo class.
Individual clubs have their own rules on what colors are allowed, and whether patches or embroidery are acceptable. Judo gis are usually plain, with limited branding, and perhaps a large back patch to represent the competitor and the country they compete for.
There is a longstanding joke that BJJ gis look like they belong on a NASCAR track because of the amount of branding and patching on them.
In short, a low cost judo gi will do, in a pinch, for BJJ. However, before you spend money on a gi, talk to the instructor at the club you are training at. They will be able to tell you the rules at their specific club.