We know there are not a couple jobs on lotro that have pets but we have no idea how strong/weak those jobs are. I do not want to spend a couple months getting to level 30 only to kick myself for picking the wrong race or class.
My first class that I took to was the hunter. I ended up enjoying him because of his self-porting ability. He travels all over the place doing errands for me.
I liked the captain next, because of his melee abilities. I found him to get stronger and better in the higher levels. I enjoy playing him a lot now.
The minstrel is the next class I liked. I have never minded the healing role, so that was just fine for me, but LOTRO minstrels are great at leveling. All their high-dmg attacks are instant or close to it, and ranged. You can take something out before it even hurts you.
I recommend players try them out also. Pick a name you like because you never know if you will not decide to keep that character. And even if you want to play another class, just keep it around until you will not really ready to delete it. Like me, you may find yourself like all the classes and characters you have created, to the point where it is hard to delete them.
For classes, I am of the opinion that hunters are one of the easiest to solo with just due to the skills they get that make them reasonably self sufficient. Yes you are a little squishier than a heavy armor class but having track and the ports makes many things easier and using traps wisely can help with the squishiness, just have to play smart to counter it. I have heard Loremasters are very good solo's as well but I've never gotten one past 12 yet so I can't confirm that.
Eg I love the fast dps of a minstrel but I can't go up against 3-4 equal level mobs since I don't have an aoe attack or heavy armor like champs (and probably guardians -- haven't played them to know but i figure they should have some kind of aoe attack). Additionally, even comparing my limited gear set as a champion, I have not seen other same-level champions fare better because of their increased defense rating -- i.e., they did instances or bought or made better gear to wear, often adding 500-900 more armor points than i might have.
Taking your classes individual skills, you can do some things. A pet class can often do some quests because of running in and tagging some quest item while you are not pet handles the monsters around. A hunter can trap several targets and take them out as he needs.
And we know that wardens and rune keepers seem to have an above average dps, also depending on each character's gear set, I am sure.