Gloves
The key is that the glove doesn't weigh so much that the player can't control it. It needs to be big enough to catch the ball, but not too heavy. The other key thing with gloves is getting one that is soft. In the past gloves were hard leather that took months/years to break in. That is still the case with some models, but you can find pre-softened leather gloves and that is a huge advantage for the girls. Mizuno gloves are good options but find a glove that works well for the player. You and your daughter should go try them on and find one that fits, she likes and is the right color. Try all brands/models. Also when you are looking for a glove, take a ball or find a ball that is the correct size at the store and make sure it fits in the pocket. A 10 inch ball will get lost in a 12 inch glove so make sure she can control the glove and the ball fits snuggly.

8U Players - the key is to buy a glove that will last a couple of yrs as they outgrow the gloves before they wear them out. For this age I recommend a 9" or maybe a 10" glove. Most gloves will show the size somewhere on the glove, most of the time in the pocket or the model reflects the size. For example Mizuno gloves do both…an MVP1050 is an 10.5" glove.
10U Players - I would recommend a 10", 10.5" or an 11" glove. Again, pre-softened is best.
12U-14U Players- I would recommend an 11", 11.5 or a 12" glove. Your could go to a 12.5" glove if your daughter is strictly an outfielder…infielders should go with a slightly smaller glove. Again, pre-softened is best.

Catching Mitts
There are a number of companies that make fast pitch catching mitts. Probably the top of the line are Nikona gloves. These will be a little stiff at first but with a little Nikona glove oil and some time they break in nicely. The Nikona's are a bit pricey ($150ish) but these are gloves that will last 5-20 yrs depending on use and care. Mizuno also has a good catching glove as does Wilson, Easton, and Rawlings. Just make sure they are for fast pitch and not baseball. The fast pitch catching gloves look more like a first baseman's mitt than a catchers mitt.

Bat Types
Bats are provided for the league but most are pretty old and very old technologies. There are basically three types of bats on the market today: 1) standard metal bats that run between $30-100, 2) composite bats (models include Easton Synergy, Easton Stealth, Combat, DeMarini, Worth Quad, Mizuno) that are made of graphite composite materials and will run from $100-$300, and 3) end-loaded bats with Rockettech's being the most popular and they run from $200-$250. The advantages/disadvantages of the composite vs. end-loaded bats will continue forever but here is one opinion: the composite bats are easier to swing as the weight is evenly distributed from the handle to the end, therefore for the smaller younger girls they are easier to control. The downside on composite bats are that I have seen a lot of the composite bats break or crack at the handle and the bat is pretty much done. You can return them for a new bat if it within the warranty period and Easton has been pretty good about returns (I think they have a 1 yr warranty).
The end-loaded bats have more pop then the composite bats. I have seen a lot more harder hit balls with end-loaded than composite bats but end-loaded bats are also less forgiving. A girl needs to have strength and a good swing to swing an end-loaded bat as the weight is out on the end and this will cause the girl's hands to extend outside the ball (which is bad).
So my recommendation is to start with an metal or composite bat until they prove they are big enough and capable of swinging an end-loaded bat…..and that ability comes from using their entire body to swing vs. just their arms..quoting a well-respected hitting coach…"a girl that only swings with her arms can swing a branch…but a girl that swings with her legs, bottom and arms can swing the entire tree"

Bat Sizes
The key with a bat is the ability of the girl to control the bat. The common mistake is to buy a bat that weighs too much or is too long. Bats are typically sized by length and weight, e.g., 31/21. The difference between length and weight is called the drop, e.g. a drop 10 bat means that the weight is 10 ozs less than the length in inches.
8U - I would recommend trying out a few of the bats the league provides before buying anything. Once you see her swing a few of the bats the appropriate size will become apparent. Do not buy a composite or end-loaded bat for an 8U player!!! The appropriate bat size will be something like a 26"/16oz or 27"/17oz.
10U At this point the player may have played a year or two and will have grown a little more. For 10U they should be able to handle a 27 to 30" bat with a weight of 17-19 ozs. For the stronger players you can start to consider the higher end composite bats..and possibly an end-loaded bat if she has a good swing and is strong.
12U - They should be able to handle a 28 to 31" bat with a weight of 17-21 ozs. For the stronger players you can start to consider the higher end composite bats..and possibly an end-loaded bat if she has a good swing and is strong.
14U - They should be able to handle a 29 to 32" bat with a weight of 19-22 ozs. For the stronger players you can start to consider the higher end composite bats..and possibly an end-loaded bat if she has a good swing and is strong.

Sliding/Protective Gear
Most of the players will wear compression shorts (thick, padded short that covers the bottom and thigh area) under their shorts or pants. These protect the girls upper thigh/bottom when they slide. Also, a lot of the girls will wear sliding pads on one or both of their legs to protect knees and lower legs. Some kids like short knees pads that cover only the knee, some like long pads on both legs that cover the knee and lower legs and some like one of each. The pads and compression shorts can be purchased at most Sporting goods stores