There are many many different ways to approach rain barrels.
After looking at lots of different systems and a little personal experience, I have developed a favorite.
60 gallon barrels are less expensive than 300 gallon totes even when you account for the water they hold. 60 gallon barrels can often be found for free and are easier to get in the car. 300 gallon barrels are a little easier to deal with in that you have less pluming, fewer spigots and potential leaks. We have some of each.
Your roofing material will also matter. If you have a metal roof, you will be able to harvest water even with a light dew. If you have a flat tar and gravel roof, it will take a fair bit of rain before the water will starts to flow. A light rain might produce 100 gallons on a metal roof and nothing off a flat tar and gravel roof. We know because we have both.
If you are using 60 gallon barrels you are going to want more than one. A good rain can fill a 60 gallon barrel fast (less than one hour). It will also empty very fast. For example five plants in your garden taking 5 gallons each means you will be able to water 2.4 times before its empty. We have around 1,200 gallons of storage and it still gone before the end of the summer.
So how to connect them? This drawing is based on a good system with a few of my own improvements. Barrels normally have holes already in the top for filling, you can use the holes to thread in pipes. This saves drilling and allows for tighter connections. Many people connect them on the sides but its really hard to get a seal on on curved surface. Having a funnel a bit higher than the rest of the system allows for the following: a simple way to keep out leaves and insects, vent air from the system, to fill the barrels to the very top. The elbow at the end keeps the water from existing before all the barrels are filled and when you daisy chain them, there is only one overflow to deal with. You can connect as many barrels as you like this way. Dont forget to include some unions so you can take the barrels apart for cleaning & repairs incase one of the spigots develops a leak. I have also looked at systems where the barrels are turned upside down and the connections are on the bottom. Its really easy to forget that the rain barrels are on because they are silent unlike municipal water which is under pressure and reminds you with its gurgles and hisses. I admit I have emptied hundreds of gallons forgetting my barrels. By connecting at the top, you insure that user error or a leak wont drain the entire system.
More on Rain tote systems when I have time. Good Luck!