How large should my bucket/container be?

You have several options here.

First,are you going to be using a bucket?
A rubbermaid container?
Or something else?

The easiest size bucket to maintain would be a five gallon bucket. These are the common size used by most people who decide to grow using the DWC method.The smallest size I would recommend is the 3.5 gallon buckets if this is your first time growing in a bubbler. If you have already had some experience with this method,you could try using the 2 gallon size buckets. Just remember that the smaller the bucket, the more maintenance will be reqiuired.

A 2 gallon bucket will require daily maintenance to top up the reservoir as the nutrient solution evaporates and transpires.
The pH and TDS of the nutrients will also require daily maintenance. The 5 gallon buckets are more stable for the simple reason that there is more volume there. So just keep that in mind when choosing a bucket size...the larger the bucket, the more pH and TDS are stabilized and less topping up.

Smaller sizes are less pH and TDS stable and require frequent topping up.

One final note is on bucket color.

The darker the bucket, the better. Black buckets are perfect for DWC as they dont let any light into the container which can lead to algae growth.
If you cannot find black,use the darkest color you can find. If you choose the white buckets, wrap the buckets and lids with several layers of duct tape or anti-corrosion pipe tape.