Use an exhaust fan instead of a hood in the kitchen

When calculating the minimum size of a range hood, there are three things you should consider. The size of the cooking surface, the amount of heat produced by the cooking surface, and the volume of the kitchen.

If the range hood is attached to a wall, you should have 100 cubic feet per minute(cfm) per linear foot. So if you have a 30" wide range, you should have a hood rated at 250 cfm ((30/12)*100 =250). If the hood is over an island, you'll use 150 cfm/linear foot. In this case that same 30" cook top, would require 375 cfm ((30/12)*150 = 375).

Next we'll determine the minimum capacity based on British thermal units(BTU)/hour, by dividing the BTU/hour by 100. For example, if we had a cooktop that produced 40,000 BTUs, we would need 400 cfm. If you are using an electric range (measured in watts), simply multiply watts by 3.41214163 to determine BTU/hr.

The final calculation, will be based on the size of the kitchen. The air in the kitchen should be cycled 15 times per hour, so our formula will be ft³/4. If we have a 10ft x 10ft x 8ft kitchen, (10 X 10 X 8)/4 = 200 cfm.

We'll then choose the largest from these three calculations, and that will be the minimum size hood we need. If you are doing more cooking than the average person, or just want a little more air movement. You can always get a larger hood, this is just the minimum size you should consider.

International Residential Code (IRC), says the minimum intermittent exhaust rate for a kitchen is 100 cfm, while the minimum continuous exhaust rate is 25 cfm.

M1507.4 Local exhaust rates. Local exhaust systems shall be designed to have the capacity to exhaust the minimum air flow rate determined in accordance with Table M1507.4.

So you'll want to make sure the hood is at least capable of achieving these flow rates.

There's no reason you can't install a hood on the brick, it will work fine. You need to buy one designed to hang on the wall, not the ceiling, and there's loads of choices either way. You can run a power line up from behind the range and hide it with a splashback. I highly recommend a splashback instead of having bare brick as it will be much easier to clean food off of.

As for ducting it completely depends on the construction of your home how possible it is to do, and how cosmetically pleasing you can make it. It's not possible to say without more detail.

Before making any decisions you should check your local building codes, some areas mandate you have to install a duct, others don't. Some mandate you can't have your range in certain places. It would stink to build your kitchen and then find out it's illegal!