Since you are on blue, this is easier to solve. From levels 1-40, it is usually better to melee on a Shaman instead of using your DoTs. You correctly point out that Shaman damage spells are pretty bad early on.
You should haste yourself, slow the enemy, and melee the mob to death. This will be more mana efficient than using your DoTs, since you are only spending mana on slow and maybe malo if they are resisting your slows. Healing yourself after tanking the damage is also generally more mana efficient, since it cannot be resisted, unlike your DoTs.
Here is a list by level of what you should get weapon wise. This changes after certain levels due to the damage caps designed to limit how powerful a weapon is. Shamans use the Priest Table found here:
https://wiki.project1999.com/Game_Me...bat_and_Damage
Levels 1-9:
https://wiki.project1999.com/Smoldering_Brand
Levels 10-19:
https://wiki.project1999.com/Guard_Captain%60s_Mallet (If you want to be lazy and stick to Smoldering brand until level 20, you probably could do that. If you want an upgrade, this is about the best you can get for cheap).
Levels 20-29:
https://wiki.project1999.com/Poison_Wind_Censer
Levels 30-45:
https://wiki.project1999.com/Granite_Face_Grinder
To farm the money for your weapon, go to Misty Thicket and kill Halfling Guards at the wall. They are good XP too until level 40. Deputy Felp and Deputy Looh are alone at the opposite ends of the wall, and should be fairly easy for you to do. They drop a 10pp spear 100% of the time, and are on a 6 minute timer.
When you need to sell, you can sell in Runneye if you haven't killed any Goblins in Runneye since the 2.0 revamp. There are a few merchants near the bottom of the zone, as well as a banker. You should be apprehensive to the merchants. The banker is on a different faction, but he won't attack you as long as you don't sit down in the banker room. You can bank at a banker even if they con scowling ready to attack. I would bind at the merchant and gate whenever I was full on spears. You should become very familiar with the layout of Runneye, and be able to run out fast back to the wall.
EDIT: Also buy a cheap haste item, like
https://wiki.project1999.com/Silver_Chitin_Hand_Wraps . At level 29 you get your first haste spell,
https://wiki.project1999.com/Quickness . With gloves and Quickness you will have 52% haste, which is pretty nice at level 29.