There are many options when it comes to PVC pipe - pvc, cpvc, ul ratings, thin or thick walled, classes, and schedules - but you don't need to sort through it all for PVC gardening projects. You're not running a potable water line, putting water under pressure, or building a raceway for three-phase electric. For garden project purposes, the two PVC options are electric conduit (usually gray) and plumbing conduit (usually white). Both are readily available at many hardware stores as well as Lowe's and Home Depot.
We use 1/2" pvc pipe with row cover, but use 3/4" pipe for almost all the garden projects. The electric conduit is slightly less expensive than PVC ($2.33 vs $2.68), but it comes with a bell-shaped female end which is used when attaching several pieces of conduit together for running electrical lines. The bell usually needs to be cut off for most garden projects. The image below shows some of the common PVC fittings.
There are scores and scores of different pvc fittings on the market, but for garden projects you'll most likely be using elbows and tees. You'll find most of the fittings in the plumbing aisle but the electric conduit aisle has some useful hangers and brackets. The different sized fittings are marked in color-coded boxes, but if someone takes a fitting out of the box, they don't always put things back where they belong. If you're not sure what size the fitting is, the pvc pipe is stamped with the size along its length so grab a piece of pipe and make sure the fitting fits.
You don't need any glue or pvc cement for most garden projects. A big plus with using PVC is being able to take the projects apart for storage, and you won't be able to do that if the joints are cemented. Some of the fittings may look identical in size and shape, but they might be threaded, so look inside the fitting to make sure it's smooth without threads. There's also adapters or reducers that may have two different sized openings so check that each opening is the same size.
If you don't have a hardware store nearby and need to order the PVC pipe online it may not be very cost effective due to the shipping costs for the pipe. Amazon has the tees and elbows, but it looks like they only sell two-foot sections of PVC pipe. Prices for PVC fittings vary widely and might even be more expensive online than in a brick and mortar store like Lowes.