........... which class whould have the smoothest leveling experience for going solo and why?

I can only speak for Midgard as I do not play Albion or Hibernia. In Mid there are several classes for leveling solo:

1. Cave-Shaman with AOE DOT => Infect a whole spot of 5-6 green or blue mobs with the AOE DOT, then run away while the following mobs suffer from DOT every 4 seconds. Then move around, cast another AOE DOT on them if necessary and continue running away until all Mobs are death.
Now return and pick up all the loot lying around. You can get rich fast with this kind of "strategy". Saw a shaman doing this in DF lately. He pulled dozens of Plated Fiends and was just running away until the plated died. Then he collected a lot of seals and money. Don't try this in narrow dungeons. You need plenty of space to run away after using the AOE on the spot.

2. Thane: You single pull yellow to ora mobs with your bolts, when they arive, you cast some instant damage. Then you use your sword/axe/hammer styles to finish the enemy. Also, you have some self buffs that helps you a lot and can wear chain amor. But after every pull you need to rest a minute or so.

3. Bonedancer or Spiritmaster: Well, that is self explaining. Let your pets do the work while you sit in the background and reg mana, heal, buff or debuff.

4. Skald: Like the Thane, you have some self buffs. But you can also choose between a speed song that lets you move fast from one area to the other, a combat song that gives you additional damage and a health song that lets you reduce the down time after a fight. Also you can wear chain amor and not just studded like the Berserker which gives you more amor factor. But you can only wear a small shield, so I would suggest using a two hand weapon to do additional damage.

You can also solo with Berserker or Warrior but you would need some throwing axes to pull. Soling with Stealth classes like shadowblade or hunter is not so much fun in my opinion. These are pure RvR classes.

If you want to use your character in RvR and not only in PvE, I would suggest to try a Shaman or Skald. Needs some time to get used to it and the many heals and dots and instants and AOE and stuff. But both are very powerfull in PvE and are welcome in RvR. If you are a beginner, start with Skald. Way easier to play than Shamy.

smoothest solo imho:
1. Deathsight Necro ... never have mana problems pulling continously
2. Bonedancer ... Bone Army - kite with dots and melee pets, Suppression - tank with inst lifetap and healpets, not too hard on mana
3. Cabalist or Enchanter or SM
4. Cave Shaman or Nature Druid

aug Healer - buffs, pull -> cele - heal after fight, rinse repeat, zero downtime
DS Nerc after lvl 20

Hm, i dunno about mana reg rates and downtimes about casters yet. Anyway, I ´m more focused melee player then caster, no order in list:

Valewalker
Warden
Champion
Reaver
Minstrel
Necro (probably best killspeed in that list)
Skald

Friar imho, granted they need some levels on them but you could say that about a lot of the classes.

I would say 30+ they are one of the best solo melee types.

Solid self buffs / basic heals / self endo / good evade.

Very little downtime and once you can get some Dodger on there - they become excellent.

Good solo farmer later on, like the energizer bunny, they don't really need to stop