Using "something"is good.  
Choice is as much based on mess, ease and cost as effectiveness - as most systems that work at all work well enough in most cases.   

Usually Rth_sa (thermal resistance heat sink to air) is the main factor.   
Rjc (junction-case) is set by the manufacturer and is usually good enough if you do your part OK.  
Rcs (case-sink) which you are asking about here is usually not the major factor as long as you do it half well. It's usually only in super high power applications that Rjc and Rcs matter crucially as then Rsa needs to be very low and the rest start to matter more. 

As well as what you mention you can get thermally conductive rubber washers - these are what I usually use and they have the advantage of electrical isolation as/if desired. 

The advantage of any jointing method designed for the purpose is that it provides intimate contact with heatsink and device and avoids air voids. Air is a poor heat conductor and quite small air voids across a surface can noticeably increase thermal resistance. Using no compound etc makes consistency harder to obtain. 

Manufacturers provide data on performance but you can easily check by making several devices which are the same except for jointing material, running each at the same and highish wattage and measuring device to sink temperature drop. If you can comfortably touch the IC at full cry when temperature has stabilised it is usually OK enough - under 55 degrees C case if you can hold a thumb on it for many seconds. For first test dab with a wetted finger or other material - to avoid leaving skin on the device.

A mere whiff of forced air flow makes a vast difference to heatsink performance. In purely passive systems working on helping air flow can also help muchly. Avoid arrangements which block flow unnecessarily. 

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If you intend to mount the heatsinks as per photo, strongly consider not doing so. In an ideal vibration free environment they may last OK but in most real world conditions that is risking fracture of the leads with time.

Better would be a single heatsink on one side extending down to the PCB and screwed or otherwise anchored to the PCB in some way. Even attachment with eg neutral cure silicon rubber would be better than waving in the breeze. A single heatsink may also give some gains in heat transfer per area. Mount the TO220 device with short leads near the PCB so the majority of the heatsink is above it.