There is no standard mounting or vent hole dimensions for these type of microwaves. Although most of them adapt to 4inch vent hose, there is no standard to where on the back of the microwave the vent is attached, and this can effect where you need to cut your hole in the wall, especially in 2X4 walls where you won't have a lot of room to offset the vent.
The "traditional" way to do it is, as you have suggested, to cut the bricks out by hand (and refit the cut bricks once you've done to give a tidy edge). It can be a time consuming job.
The more usual way to do it once the lintels are in place would be to use a disc cutter - usually a petrol driven one - (aka a rotary cutter or Stihl saw, after the common brand) with a diamond-tipped blade to cut through the bricks. This will make a lot of dust. You can get a water pack to reduce the dust (and cool the disc, reducing the wear on it), but it can still make for a messy operation, as the water will make the dust into a slurry that the disc will spray about.
You can hire the saws from pretty much any plant hire outlet, who will also hire the diamond tipped blades, charging you per milimetre (or half milimetre) of wear. That can be expensive though, so if you've a lot to do, it might be cheaper to buy the diamond-tipped disc from an independant supplier.
I've also seen what is basically a chainsaw with a diamond tipped chain for cutting through walls, etc, but I've not actually seen one used to comment as to how effective they are.
Don't forget that you should use eye, ear, and dust protection if you're doing work like this.
Best Answer
It is entirely possible to construct a 6 inch hole in brickwork. The problem with a round hole rather than a square hole is where the hole cuts across joints in the masonry leaving small triangular pieces of masonry over the hole. These tend to be fairly week so are best avoided. You would therefore have to position the circular hole carefully so that is best placed not to leave small or week sections of masonry. As mentioned in other answers to get a good hole, a diamond or similar circular hole saw is the best way but at this diameter you made need a large pillar drill rig to use the hole saw and this may need to be bolted to the wall prior to making the cut.
If you can fill it a square hole then may be better. Given the diameter of the hole you are suggesting you shouldn't have any structural problems as long as you aren't right next to openings or corners in the wall. The key is to make sure that the hole doesn't leave a whole brick unsupported from below when you make the hole and with a 6" diameter this shouldn't be a problem unless your bricks are very small. The neatest way of doing this is to cut out the edges of your hole with something like a disk cutter and then use an impact hammer to chisel out the brickwork in the centre. This should leave a very neat cut.