Go grab yourself a stack of 100 Cure Serious Wounds potions from the guild potion vendor, and keep them restocked between adventures. This will be a life-saver in early levels and critical if the cleric dies or runs out of magic points.
If you're a rogue or artificer, ask a guild officer for some +5 thieves tools. Keep two stacks in inventory so you'll always have a spare and not use your last tool in an adventure.
If you are a spell-caster, be sure you keep components (standard and special) in stock. When you get new spells when leveling, go buy the right components.
You should have received a Necklace of Contemplation from WelcomePack upon joining the guild. I doubt you'll find a more useful necklace at these early levels! And when it starts to become obsolete, please lock and bank it for your next life. It really is that useful.
Feather Falling (perma- not clickie) is incredibly useful. An item of underwater action should be kept in inventory to be swapped to when needed.
Speed or Striding items will be helpful, seek at least in the 10%-20% range for striding bonus.
If you are melee, begin to look for Deadly items and do your best to keep them up to date with your current level.
Stat bonuses aren't especially powerful yet; but you might want a STR or caster-stat related item anyhow. At low levels, wizardry items are more beneficial than stat bonus and false life items will be of more beneift than a CON item.
A good all-around weapon that is easily crafted would be Acid (Burst) of Bleed. A ghostbane weapon will be handy for ghosts and wraiths. If you can get an adamantine bludgeoning weapon, keep ahold of it for when you can get shards to make it construct bane.
Keep up your stack of 100 Cure Serious Wounds potions from the guild potion vendor, and keep them restocked between adventures. They may no longer be quite as beneficial and seem to disappear quickly on melee classes running without proper divine support, but still ease the burden on divine spell points and can be enough to chug between fights to keep you alive in an emergency.
You will be starting to run into quite a few mummies. Carrying stacks of guild potions of remove curse and guild potions of remove disease will become quite useful.
Resistance items will be even more helpful. A topaz of fear immunity is worth a store purchase with some of your hard-earned points from favor to reach this level.
Time to start seeking stat items. Especially CON items begin to make a significant difference on a first life. Try to keep a greater false life item equipped as well. Other stat bonuses to consider: STR, caster stat (ie WIS for divines, CHA for sorcerer, INT for wiz/arti).
If you can find paralyzing, banishing, and disruption weapons, these are your best choices for upgrades. If you don't have Spectral Gloves (ML11) or the Cloak of Invisibility (ML9) from the Tempest Spine Raid, a ghostbane weapon will still be useful but by now most undead should be approached with a disruption weapon or a +1 Holy weapon of Undead Bane.
You'll likely meet aberrations before evil outsiders, but you'll find many of both in these levels. While banishing weapons might be the best, if you have a good alignment and are lucky enough to find one (or have the 90 divine crafting levels to make your own), a Metalline (BTA) weapon of Pure Good would be handy to have. Consider also a Holy Byeshk weapon of Aberration Bane (again likely to depend on crafting levels/materials).
When you can find groups to run with in the Tempest Spine raid, you may find your first especially useful raid gear items.
Hopefully you've found banishing, disruption, and smiting weapons by now. If you have high crafting levels, consider making a Holy (Burst) weapon of (Greater) Evil Outsider Bane on a cold iron weapon blank with a red slot to hold a Ruby of the Vampire Slayer (making it silver as well) or a silver weapon blank. Be aware you cannot banish demons in Amrath or in the Vale of Twilight Raid. If you plan to run House Cannith quests, a smiting adamantine weapon would be the ideal for that locale.
Nice named gear for this level range is most often found in Gianthold, the Orchard, Eveningstar, or the gear from House Cannith.