Adult ponchos at
Disneyland cost $9 each. We didn't buy any; someone just mentioned it to me when they were complaining about the rain on Friday. Don't know what the kid prices are.
Rain can be good for thinning the crowds, but it's deceptive to tell people the park will be "empty." Other factors come into play, such as time of year (you'll probably be fine with those dates though) and what rides and shows you actually want to experience. Also, crowds may be smaller, but rides don't necessarily run up to capacity and with some rides and attractions closed people's choices are more limited and, therefore, some ride lines can be bloated.
I can tell you what this past Friday was like. There was lots of rain. It poured at times and rained steadily for long periods of time. There was thunder and lightning. I have never seen so many people at the Tough to Be a Bug Movie

. Admittedly, this was the end of spring break, so vacationers who had spent their money already were going to come probably despite the weather. Some locals clearly showed up as well as the Buzz Lightyear and Toy Story scores would attest to.
The park was not "empty." Thinned crowds, definitely. Way better than a regular spring break day, definitely. Shorter wait times in general, absolutely. Just don't go in expecting to walk onto everything. There were still hours during the middle of the day on Friday when Tower of Terror ranged between 55 and 75 minute wait times, even during heavy rain; it is indoors after all. Toy Story still saw 40-45 minute waits for large chunks of Friday, even during the rain. By evening though, the wait time varied between 20 and 25 minutes which was great and clearly an effect of decreased crowds due to the rain. Space Mountain got up to 40 minutes at times, but since it was spring break that should have been more like 60-70 minutes. Peter Pan saw waits of 20-25 minutes but would normally be twice that. The rest of Fantasyland looked good, and you really could walk onto a lot of the rides there throughout the day. Walking around the parks was much easier than usual for such a busy time of year since fewer people overall meant less congested walkways. Lots and lots of puddles to soak feet and pant legs though. Again, these are just some examples, and crowds this past Friday were going to be higher rain or shine than they will be for your dates.
Certain things will not happen in rain. Teacups and Alice in Wonderland close. If rain is heavy and prolonged enough, Gadget's Go Coaster in ToonTown closes (it was closed Friday afternoon). Weather got bad enough this past Friday, they closed Screamin' briefly. Normally they will run that even in the rain; I expect it was the thunder and lightning that dictated that closure. Parades will not happen. Meet and Greets decrease in number but don't stop altogether. You see fewer furry characters, and the meet and greets move indoors. Fantasmic goes on if it was scheduled and if they can get the stage dry enough in time. Fireworks happen in light rain, but if there is wind they will be canceled. WoC also plays in the rain but can be canceled if wind and rain are severe enough. Most rides really do stay open but may not be as enjoyable to ride in the rain; that's a personal tolerance thing I would think.
That far out, I wouldn't worry that the weather report is accurate. Just prepare yourself for the idea that it might rain, and decide to make the best of it whatever happens. Extra socks and/or waterproof shoes for the parks, extra dry clothes back at the hotel, and an afternoon break to regroup are all good things to plan on. There are plenty of places to duck into to wait out little storms while at the parks, and I seriously doubt you will experience weather conditions as intense as they were this past Friday since that seemed atypical for this time of year. A few showers won't be that great a deterrent to enjoying the parks and will probably thin the crowds some.