Hi, Sean. One suggestion would be to build it out of wood. Brick work is possible for the do-it-yourselver but probably not a good place to start. If working with wood, you will probably need to buy tools, such as a circular saw and electric drill, that you will more likely use on future projects. The same is true of techniques. Building a wood planter will give you some experience with the basic practices that you will probably have to use again. If working with brick, your outlay for tools will probably not be as great but you will probably rarely use them again.
One possible problem might be weight. A brick planter will need a good foundation and it will be hard to remove if you change your mind in the future. This assumes that your patio is at or near ground level. If your patio is above ground on any kind of wood foundation, you could be asking for big problems in the future. Pardon me if I am misinterpreting your skill level and background from your post.
If you do build a wood planter, be sure to choose woods that will last outside like pressure treated pine, cedar or redwood and be sure to wear a dust mask when sawing them. And be careful when learning to use power tools. Be sure to read, understand and follow all the safety rules that come with your power tools.