Congratulations on reaching Level 120! There are a myriad of new things to do. The first thing you should do is head to your faction hub ship where you have been doing your mission table quests and footholds to pick up and complete the quests necessary to unlock World Quests. World Quests will provide you an opportunity to grind reputation levels, acquire gear, and gather Azerite. There are tons of new things to do that we will cover in our Level 120 Battle Guide found here: Level 120 Battle Guide.
At 96 the standard wisdom is to immediately drop what you're doing and proceed to Spires of Arak and do the quests to unlock the Inn, granting a further 20% experience bonus while in that zone. You'll want to do that eventually anyway, but I'm not sure it outweighs the quest experience from Gorgrond. However, if you decided to go to Spires immediately at 96, restrict yourself only to bonus objectives and again leave Treasures until you're 100+. Make certain that when you being the quests to unlock the inn, you speak with the quest NPC to also learn Archaeology, since it's required to collect several of the treasures in Spires.
Most heirlooms only work in a limited level range in their default form and must be upgraded to work at higher levels. That costs gold, and you’ll need around 30,000 gold to outfit yourself with a fully upgraded set (counting only those that give you bonus experience). You may need to spend some time on a boosted character to acquire the gold you need to outfit another character with heirlooms, but it’s well worth the effort.
A common mistake of new players is to upgrade their gear at every opportunity, paying for a new piece even if it will only add one or two new stat points over an existing item. Likewise, investing in headgear, neckwear, trinkets, and rings at the earliest available levels can also consume valuable cash. While it might seem foolish to leave an available slot empty, you will eventually find something to fill it. Blizzard will see to it via the quest rewards you'll get along the way. In the mean time, the 1 or more you save will serve you well if you invest it wisely. The bottom line is that one can easily level all the way to the maximum relying on just quest/drop greens. The gear you get from regular questing can help you perform well in dungeons, which gets you even better equipment.
The most simple thing is TradeSkillMaster. This AddOn shows you quite an amount of information in the items tooltip. In my opinion, DBRegionMarketAvg the best source. It tells me the price, an item was posted on all EU realms in the last 14 days. Why not DBMarket? DBMarket only shows you the items value from your server in the last 14 days. This value often gets manipulated. Some people start to post an item with a 500g value for 500.000 Gold on the auction house for several weaks. As a consequence, DBMarket is rising towards 500.000 Gold. If you use DBMarket with 100% and post your item for 500.000 Gold, nobody will buy it.