First off, you are definitely on the right track looking at higher CFM. If you peruse the threads on this forum there is a lot on how to figure the right amount for your setup. For what it is worth I have both internal and external blower, in different homes - the external is a fairly short distance, on the roof without a silencer - and the internal blower is much noisier. There's also baffle noise which you can't really get around. What type of makeup air system are you planning? Because if it's an active system it, too, will make noise regardless of your hood blower. All quite complicated, and it is tough to know what the actual outcome will sound like once you take into account all the variables.

300cfm is likely listed because that level of exhaust doesn't require any complicated and often expensive makeup air system.

To summarize past messages, 90 CFM/sq.ft. x 6 sq. ft. = 540 CFM actual (required). Blower rating at zero static pressure should be 1.5 times that* or 800 CFM or higher. Noise can be reduced if the external (wall) blower (like a down roof blower) is oversized and operated at partial power. Noise increases as some power of the blade tip velocity.

Aim for a duct velocity at required flow rate toward the 1000 ft/min end of the 1000 -- 2000 ft/min recommended range. If you use rectangular ducts to fit in the joist space, go large enough.

*MUA [complexity] depends on presence of combustion appliances and house configuration. The more restrictive the MUA, the more the rated hood CFM needs to be raised to achieve the required CFM.

Thank you all! It sounds like an external blower in the 1000 CFM range would be appropriate for us, and allow us to mostly use it in a lower power range that is less noisy.

I'm still thinking a MUA. We have a 150-year old home that is certainly not tight, and our gas-fired furnace is in the basement on the opposite end of the house. We also live in a cold climate. Any general advice? Or should I consult an HVAC person?

While a leaky house helps at low CFM, it isn't going to suffice for higher levels, drags in stuff you don't want, and allows too much depressurization of the house to avoid back-drafting. It is also high enough for building code requirements to apply. However, if your gas furnace is provided with its own MUA (kits exist for this, usually), then you can likely operate with "passive" MUA, which is a 'hole in the wall with a filter' supplemented by some heating. If the gas furnace can't supplement its heating duty sufficiently (and most home furnaces don't expect to solve winter 'with a window open'), then electric heating may be needed, or even a gas heater. Here is where HVAC is needed for specific advice.

Below is a plot of required supplemental heating as a function of CFM and differential temperature (inside vs. outside). Note the CFM is the actual CFM, and not the blower rated CFM.

As may be apparent, if you want the interior air to be at 70 degrees F and the outside is at 0 F, then the yellow 70F line at 500 CFM corresponds to about 30k BTUh of needed MUA air heating. If the furnace doesn't have enough excess capacity, then auxiliary heating -- electric or gas -- is called for.