Being a friar myself, I agree :) Friar is a great class for soloing. All classes in DAOC can solo if specced properly - friar just happens to be one of the most fun ones, IMO. Necromancer is a fast leveling class if you like to watch your pet fight. I haven't played the other realms much, but I like the Valewalker class of Hibernia for soloing also.
Don't start a light tank or a rogue character if you want to solo easily. Light tanks can be powerful in groups but suffer from the light armor that goes with their class. They have no buffs or heals to help out like the friar. Rogue classes also suffer from weak armor and weak attacks. Lots of their most powerful attacks and attack chains are positional - hard to get off when you're soloing.
If you like to play a caster, the sorcerer is a strong class. It uses charmed pets and you can charm a pet up to your level, which makes the sorcerer pet one of the strongest in the game if you choose the right one for the job.
Theurgist is another strong pet class. Multiple pets can be cast so you can set up staggered lines of defense so that if the mob comes toward you, the second line can still cast.
These are all Albion classes (except Valewalker). Hopefully, someone from the other realms will give you some insight into Hibernia and Midgard.
I agree that the coop server, Gaheris, would be a best bet for you if you don't plan to participate in RvR. You can have up to 24 characters on that server (8 in each realm). Makes it easier to get items and money from one character to another and you also have a myriad of choices of where to hunt, including the frontiers which are mostly off-limits on the regular servers because of RvR.
A good place to read up on the various classes and find guides is classesofcamelot.com. I'm sure you can find some guides on this site also, but CoC is more comprehensive, giving you guide, website and message board information for each class all in one place.
Good luck in your travels through DAOC.