I use a mix of internal & external filters.
I started with internal filters & small tanks. As the tanks gave got bigger I've moved towards external filters.
I agree with Sue that one of the disadvantages of internal filters is when it drops muck back into the tank when being removed. I have a plastic jug kept specifically for putting into the tank & putting the internal filter into, before removing jug & internal filter to avoid dropping anything back into the tank.
I'm not too bothered about having equipment in the tank, so I've been happy with the internal filters in the smaller tanks.
As for external filters, I will openly admit by love of the Fluval FX filters. I love the drain port at the bottom, which with the addition of a piece of hose long enough to reach the garden, makes draining water from the tanks so easy. I have FX4s on several tanks, and have 2 FX4s and an FX6 on the river tank (400L). There is no priming botton, just put the water in the filter, attach the pipes & switch on. these filters also switch off briefly every 12 hours to remove any air from the system. I have also put extra media into my filters. I think the FX filters are relatively quiet for what they are, though I admit that the FX6 can make the doors on the cabinet vibrate slightly, which is louder than the filter. There is no priming button, just put the water in the filter, attach the pipes & switch on. these filters also switch off briefly every 12 hours to remove any air from the system.
I also have a Fluval 306 on the tiger barb tank, and a Fluval 206 attached to the chiller unit for the axolotls. They have worked well, are quite compact, so don't take up much space in the cabinet. The priming button can be a bit stiff, and there's no drain port like on the FX, but they're great little filters.
I will admit that I use trays underneath all of my external filters for two reasons. Firstly, I know what I'm like with water, and tend to be quite "splashy" during tanks maintenance & water changes. It's relatively common for me to spill water, or forget to completely close a valve before removing a hose

The second reason is because the FX filters have little rubber feet, which makes it almost impossible to slide the filter out of the cabinet for cleaning. Having it on a tray makes it much easier.
I'm sure you'll be able to find a filter that works well for you, your tank, and your fish.
