If you have limited space to work with, an over-the-range microwave venting kit may be your best option. These can exhaust air to the outside or recirculate it.
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Range Hood vs. Microwave Vent Comparison
When my over-the-range microwave's vent fan is on, it blows hot air from the vents above it into the kitchen. Is it supposed to do that rather than out of the house?
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Whirlpool UMH50008HS 24 Inch Over-the-Range Microwave Hood Combo with 750-Watt Cooking Power, Cooktop Lighting, 3-Speed Fan, Defrost Option, Add 30 Seconds Option, Stainless Steel Interior, Dishwasher-Safe Turntable, Panel-Ready and Small Space Solution
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Range Hood vs. Microwave: Vent Hood Options