In windsurfing the right gear is super important, especially if you are new to the sport. For example, to start windsurfing a wave board or a race sail would cause massive frustration. You need to start with easy to sail and easy to rig gear. There is a wide range of all-round gear available for beginners and remember that you also need to factor in your weight when deciding.
The first rule is don't buy gear more than 5 years old and start with a smallish sail and a big / wide board with a lot of volume. This will help you understand the feel and concept of windsurfing when you first climb on, it will be easy to learn things like sail control and board balance. A short but wide board is what you need, the width provides stability and the short length offers early planing for when you progress. A good width for an average bloke of say 80kg is around 90cm at around 180L.
On the first go it's important to have a center board, or as some call it, a dagger board. This will ensure that you don't drift downwind and it will help you stay upwind. Most of these boards come with soft padding all over the deck to make it comfortable when climbing on. The foot straps need to be adjustable, meaning you should be able to take them out and place them close to the mast and then move them back as you improve, this will help you when you start planing.
A good sail size to start with is around 5.0sqm - 5.5sqm for most sailors and 5.5sqm for heavy sailors. For someone very light such as 40 - 50kg, a sail smaller than 4.5sqm is recommended. The type of sail needs to be a light and easy sail with no cambers. An all-round freeride sail is fine, even wave or freestyle sails can be used as they are designed for good control. Avoid technical race sails.
A waterstarter can be a good idea for smaller sailors, and they are cheap to buy. They were actually designed to help learn the waterstart but it's also effective at keeping the sail afloat when uphauling.
For young kids there are many package deals that offer very affordable "kiddies" rigs which come all inclusive. Just ask your local shop for a "kiddies" rig and they'll help you out. It's pretty much minature beginners gear for kids.