For starters, every class can be soloed to level 140 without too much issue. Some level slower than others, but the landscape quests are meant to be solo and you can get to 140 without trouble.
Typically, I solo all the way up to 140 and then start grouping, BUT there are certainly exceptions. If I am around level 20 or so, and I see a group calling out for level 20-ish to run the barrows, there is a pretty good chance I will join. Same if I am a level 55+ in Moria, or a level 75-ish in Dunland. Some of the fixed level raids and instances are fun to do on-level.
So in a nutshell, it is up to you and what you prefer. If you are a NEW player, I would recommend joining some groups along the way just to get a feel of how it works..... if you are a SEASONED player, it's up to you. I started playing when the level cap changed to 65 and the game went F2P, and have played group content at every level cap since, as well as being on some of the legendary servers for a time to experience fellowships on-level again...... so if you know how fellowships work, do whatever you want to do. If you are new to grouping, I would take on a few groups if you can just to experience it.
Moved from Riddermark to Arkenstone on 9/29/2015!
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Disclaimer: The definition of "Soon™" and "In The Near Future™" is based solely on SSG's interpretation of the words, and all similarities with dictionary definitions of the word "Soon™", "Near", and "Future" are purely coincidental and should not be interpreted as a time frame that will come to pass within a reasonable amount of time.