I have a Hollywood similar to this one—Hollywood Racks - 2-Bike Hitch Mounted Rack, HR200Z Trail Rider Platform Style Bike Rack - Fits 1.25 and 2-Inch Receivers https://www.amazon.com/dp/B00IHR0H1K/ref=cm_sw_r_cp_api_glt_i_G1RWF0CSWFA7WCJ2YMYF?_encoding=UTF8&psc=1 On my Outback. I found it on marketplace for $100. It has been one of the best hundred dollars I’ve ever spent. The solid design and ease of loading/unloading bikes is fantastic. I will warn you it is fairly heavy.
Most bike racks will easily accommodate both types of bikes. If your mountain bike has tires wider that 2.5 inches then there could be some fitment issues. I like Hollywood racks and prefer racks that hold bikes by the wheels and have a small part to stabilize the bike by holding the frame. Racks that only support the bike by the frame tend to cause trouble down the road with bikes swinging in the breeze or an accidental pedal placement rubbing paint off your frames.
This rack didn’t lead to complaints from those I sold it to when I worked at a LBS once upon a time. Hollywood Racks - 2-Bike Hitch Mounted Rack, HR200Z Trail Rider Platform Style Bike Rack - Fits 1.25 and 2-Inch Receivers https://smile.amazon.com/dp/B00IHR0H1K/ref=cm_sw_r_cp_api_glt_fabc_9TJHQB3JPNBWEGPZANMP?_encoding=UTF8&psc=1
You can probably pick up a used Yakima, or Thule pretty cheap used. Or even a new Hollywood on Amazon.
(Hollywood Racks - 2-Bike Hitch Mounted Rack, HR200Z Trail Rider Platform Style Bike Rack - Fits 1.25 and 2-Inch Receivers https://www.amazon.com/dp/B00IHR0H1K/ref=cm_sw_r_cp_apa_i_71LEDb6R19R4K)
My personal preference is the style where the bike is secured by the wheels.
Hollywood Racks - 2-Bike Hitch Mounted Rack, HR200Z Trail Rider Platform Style Bike Rack - Fits 1.25 and 2-Inch Receivers https://www.amazon.com/dp/B00IHR0H1K/ref=cm_sw_r_apan_glt_fabc_78JVNFMC25KRX61BYJ4S?_encoding=UTF8&psc=1
Hollywood Racks - 2-Bike Hitch Mounted Rack, HR200Z Trail Rider Platform Style Bike Rack - Fits 1.25 and 2-Inch Receivers https://www.amazon.com/dp/B00IHR0H1K/ref=cm_sw_r_cp_api_i_5VNVFbZMTDK2V?_encoding=UTF8&psc=1
Older version of this: http://www.yakima.com/shop/bike/hitch/swingdaddy I also have some roof racks, but this is so much easier - and still allows me to get to the hatch. Imgur Only down part is it does need the top tube adapter for dual suspension bikes.
edit: I've also used this one: http://www.amazon.com/Hollywood-Racks-Trail-Rider-Hitch/dp/B00IHR0H1K/ref=sr_1_5?ie=UTF8&qid=1431434232&sr=8-5&keywords=hollywood+bike+rack easier to load, but upgraded for the hatch access and more bikes.