GAME PROGRESSION
- Kill monsters until you get to lvl 6
- Invest in your Area of Effect (AOE) skills
- Progress up through the quests
- Kill Griswold and save Cain (Akara gives you a neat armor)
- Continue progressing up until Mephisto
- Farm arcane crystals (Mephisto then Nihlatak), make TUs, Upgrade your stuff
- At lvl 45 : Do the chalenge lvl
- Continue progress until lvl 80+ lvl challenge 2, it will unlock a special skill at lvl 90
- Progress up until Hell difficulty
- Complete the Easy Uber dungeons levels AND Rifts to get ubers charms
- Farm in some places to get SU, Sets, and crafting items
- Complete the hard ubers ( both dungeon and rifts!)
- Repeat until you have all the hard charms and the best loot
Alternatively: HechtHeftig's thorough Newbie walkthrough
MONSTERS, CHARMS AND LEVELING
Each areas have different monster level. It is better to kill monsters that are around your level.
Charms also have specific level requirement, here's some links to get a list of charms:
+ tsw charm list
+ Aerial's recap list (It's the text with colors around the middle of his post)
Here's the quick recap for the EXP grind:
+ EXP from lvl 1 to lvl 110: Just play the game normally
+ EXP to get to lvl 110: IotSS / A5 Red portals / End of A5 / A5 Icy Cellar
+ EXP to get to lvl 115: Torajan Jungles / Cow Level
+ EXP to get to lvl 120: K3BA / Tran Athulua / Khalimgrad / Azmodan level
+ EXP to get to lvl 125: Duncraig / Teganze / Triune
+ EXP to get to lvl 140+: Fauztinville / Bremmtown / Vizjun / Toraja / Duncraig/ Lab
Those are all the types of monsters:
- Regular Monsters → common and easy to kill
- Elite Monsters → harder, gives more loot and xp
- Veteran Monsters → dont exist anymore used to drop eyes
- Uber Monsters → common uber level enemy, hard to kill
- Super Unique Monsters → like in D2LoD, they are minibosses and bosses
- Uber Bosses → increasingly tough, drop uber charm
LOOTS AND ITEMS 
Items have specific stats that are needed to have before equipping them. Always keep a few stat point to be able to equip them at all times. Some items can only be equipped by specific chars, beware of that.
Be careful before upgrading a TU item to its next tier, as the stats requirement are steep. Check their page for a indication of their stat requirements.
Look at the dexterity requirement from Tier3 to Tier4, its a huge step. Don't upgrade before checking the docs. More in the Item section.