I'll be quite frank, I have an immediate bias toward war sloops, but with good reason. I personally adore the maneuverability of even the most sluggish builds on War Sloops, it makes them great fun and nye indestructible in PvE. In PvP, they do seem to be a weaker link depending on the Captain, though.
Let the truth be heard.. I'm not a fan of brigs. But that doesn't outweigh their usefulness, as they are overall just better versions of Galleons with an open deck that makes it feel a lot less claustrophobic. They are just a tad bit expensive, in some cases too expensive for my taste.
Frigates are not only, in my opinion, excuse my French, one of the most B.A. ship designs, I mean, they look so angry! But they are also undoubtedly useful in both PvE and SvS. Their naturally high health pool makes it great for eating shots, and are fantastic tanks if built like one! The cannon positions are also very advantageous, being able to shoot to the front of the ship is useful.
Finally, the rotten love child.. Galleons. While their design is realistically pretty snazzy and they are absolutely enormous, their Achilles' heel lies in many aspects of the vessel. Not only do they start off slow without any specific builds, but they never really get much faster unless you plan to ignore its strengths to fix its weaknesses. Their weak spots are arguably the most detrimental in combat, basically narrowing down the whole front of the ship once the hull has been broken. They feel terribly claustrophobic as stated previously, with only 10 crew spots and a narrow deck covered with walls, breeches and the likes, they just don't feel nice to steer or cannoneer from. However, I will give them this. War Galleons are tied with War Brigs for Hit Points and have the largest broadside, once again tied with Brigs.
Overall, go with what your heart and/or wallet tells you feels the best. These are just observations from myself and other users.