Upgrading the armour helps the runners come back successfully more often, and weapons determine how much they return with, so you should fully upgrade them.
Once you have Dick bringing back diamonds to sell, upgrade Tom and send him for malachite ore, then Harry for whatever ingredients you need for the strongest healing potion formula you have (or you could make potions to sell).
As Senior Cinco said, all you need to do is leave the battle tower after sending out the runners and return. I generally just teleported to the outside teleporter shrine on Sentinel Island, then use the dragon stone to go to the throne room, talk to the runners and leave the battle tower, and repeat. If you want to farm for awhile, though, it would help if you went to a small area first. On my Xbox it takes 12 seconds to enter the throne room; leaving the battle tower, it takes about 28 seconds to return outside on Sentinel Island, but only 10 seconds to return to the interior of a house in High Hall (in either case there is a 10 second cooldown after leaving the battle tower before you can use the dragon stone again).
Once you have enough gold to upgrade all the runners and visit your trainer to raise the level cap of any skills you want to further advance (and possibly unlearn your current skills to redistribute the points), I wouldn't bother doing too much more farming for diamonds and malachite.
With most merchants you will eventually start depleting their gold just by selling them excess loot. When you are ready to head to the Hall of Echoes, you can do some farming with your runners so you can clear out any remaining gold from merchants. I farmed for diamonds a couple times briefly after getting the battle tower, and ended up taking half a dozen spare pieces of equipment with me into the Hall of Echoes because all the merchants were out of gold (I sent some lower level potions and food to the battle tower chest to get them out of my inventory, but didn't want to have to sort out equipment later).
The exception to this is a traveling merchant on the path from the depleted ore mine to the harbour and High Hall, who you only meet once. You'll need at least 52k worth of stuff to sell him if you want to get a malachite gem and all of his gold, plus another 20k, or so, in case he has stuff to buy (I reloaded a couple of times, and bought a belt and bracelet to upgrade my existing equipment, and couple weapons to get the enchantments from, and sold everything I had to spare, leaving him with 2k gold).
