You don't need a heatsink AND fan. One or the other will do (if you have a fan, you don't need a heatsink).
Thermal management on the 3B+ is much improved over the older 3B model, and for many people the 3B+ will be fine on its own. If you are going to push the system hard or have the system in a warm environment a heatsink or fan might be needed to reduce throttling (the system will slow down to prevent overheating).
Even a quiet, low CFM fan will keep the system cool in a well ventilated case.
If you want to go the passive heatsink route you'll need a large one, and a very well ventilated case. The cheap tiny heatsinks marketed for Pi computers are not very effective (especially since some have double sided tape and not thermal adhesive). The Kintaro heatsink is the best, but it won't fit in most cases without some ingenuity (and even with ingenuity it won't fit in some cases).
Another option, and one I highly recommend, is the 2nd generation Flirc case
. The aluminum alloy Flirc case itself acts as a huge heatsink, keeping the Pi 3B or 3B+ cool without the noise or additional power requirements of a fan. Due to clever design, it also doesn't interfere with wireless (WiFi, Bluetooth) like some others on the market. Not that I've noticed anyway, as most of my Pi 3B/3B+ computers are in Flirc cases and connected to my wireless network. The Flirc Gen2 case includes different thermal pads for the 3B and 3B+ models.
My mind is like a browser. 27 tabs are open, 9 aren't responding,
lots of pop-ups...and where is that annoying music coming from?