Theoretically, you'd need a minimum of the top 30MHz channel plus the width of your upper sideband - but it's a relatively low requirement that should be covered by most modern scopes. A 50MHz or 70MHz base level scope would be sufficient bandwidth for that application, but it's generally not much more for 100MHz inputs (and is often software upgradable or hackable on digital scopes), and that will cover you up into reasonable speed digital buses and keep square wave signals looking like square waves - since you really want little attenuation at the 3rd and 5th harmonics for a square wave to look basically square, that would let you see 20MHz square/pwm signals without the rise/fall time of the edge being too much of an issue.
There is a lot of discussion of budget scopes on this forum, so make sure to use that search button (the icon on the top right, not the box top left, it doesn't work as well) when you start thinking about a specific model. Your budget is just at or under the low entry level price from many manufacturers, but there are some deals to be had under that or used scopes in that pricepoint that would probably be great choices - just make sure to look at reviews or people discussing the unit... on the budget end there can definitely still be stinkers.