Congratulations on both your pregnancy and the decision to cloth diaper. I've cloth diapered my youngest two (and my oldest as a toddler). For the newborn period, the easiest way to go is prefolds and covers (what your mother used). You change newborns so often that it's the cheapest and easiest way. Plus you can have a few dozen for a small cost. If you want to wash every day, 18 is a good number. If you want to wash every other day (which really is best, no matter how many diapers you have, just because you don't want them sitting with urine and feces longer than that), then 36 is a great number. A great thing they have now is called a Snappi. It's easier (for many people) than diaper pins. Infant prefolds fit to 15 lbs. After that, a mixture of premium prefolds/covers and pockets will be an easy choice. Unfortunately, different diapers work for different babies (and mamas!). Sometimes you do just have to try them and see.
A lot of people buy used, so you could either buy used to save money if you change your mind, or just sell what you don't love later on. www.diaperswappers.com and www.clothdiapernation.com are good forums. They both have a lot of discussion boards where you can ask questions about diapers and they have a For Sale or Trade board.
Pockets like Bum Genius can be one size, meaning you use them from about 10 or 12 lbs up to 35 lbs. My 2 year old wears these and Fuzzi Bunz. She's been in a size medium Fuzzi Bunz since 4 months old! My baby wears Bum Genius one size and Happy Heiney's one size, along with premium prefolds and wool covers. I also have lots of fitted diapers (have elastic and fit baby more than a prefold but still require a cover) and we use wool covers that I knit and PUL covers. BOth are basically water proof and keep the urine and poo from getting on clothing. My favorite PUL cover, and very popular with people, is made by Thirsties.
There are lots of different choices out there. Many people, though, find ease of use with prefolds as newborns (as long as you have plenty and some good covers, they are great!) and Bum Genius one size the rest of the time. There are many others out there, but these tend to be popular with most. I personally like supporting WAHMs that make diapers, but they are all different, and I think you'd be safe in using the prefolds and Bum Genius.
This is very abbreviated, as you know there are lots out there. I tried to tell you the ones that most people find to be easy. If you have ANY questions, please feel free to send me a message through Mamasource. I'll be happy to answer any you can think of. I've tried LOTS of different diapers and I've guided several people in converting to cloth.
And though it does seem very expensive at first, it is an intitial investment. IT's lots better than the $15-20 a week you could be spending on disposables, and if you have more children you can use the same diapers (ESPECIALLY the prefolds. These will last generations!). And it's oodles better for baby's skin and the environment. No nasty chemicals!!!
***ETA I read some other responses, and you actually do have to launder all the diapers (except for covers) after you take them off. Prefolds can't be reused before laundering. You should wash them each time. Covers can be used all throughout the day, just switching when they're wet to allow them to dry. Ones that get poo on them should be washed before using again.