You can go anywhere, but yes, that's the order of the zones for the Daggerfall Covenant zones.

If you need help with the order of content as it was originally designed: https://forums.elderscrollsonline.com/en/discussion/413807/what-order-should-i-do-esos-story-arcs-a-guide

For the Wayshrine, you should be able to select another Wayshrine in the zone you want to go to. Since you want to go to Daggerfall Covenant areas, chose Glenumbra. When you arrive, talk to the Hooded Figure. This will start the Main Quest, and should get you to Stros M'Kai if you are on a DC allied character. If not, I suggest you ask in zone chat for someone to port you to Stros M'Kai.

If you have completed all the quests in an area, the symbol for the area should turn white.

For leveling up, you can catch up on skills pretty quickly. Armor levels up based on what you are wearing, so I usually try to wear a mix of armor pieces with at least one of each type so the lines level. With weapons and class skill lines, these level based on what is on your active skill bar. So if I know I'm going to level bow, dual wield, and two handed, I might put a skill from each one on my bar so each weapon gets exp and levels, even though I can't use those skills without the weapon equipped. That's kind of advanced leveling though, and it doesn't take that much time to level up a new weapon skill.

Hope this helps!

For leveling skills, your XP is applied to whatever is active or being worn at the time. Once you get to level 15 you can begin to carry a back-up weapon and gain access to a second skill bar. From there, if you want to focus on leveling particular skills you can put them all on the same bar and make that bar the active one when you turn in a quest.

You really only need one bar for combat while questing if you're using the right skills, so when I was leveling up my stamblade I'd carry a destro or resto staff on my back bar and with enough quest turn-ins I eventually got them both to 50 without ever using them. Will make it a bit less painful down the road if I ever decide to switch to magicka.

This may seem like a stupid question, but what did you choose for your alliance? If you did not choose Daggerfall Covenant then you can't do it. Make sure you are DC first. This happened to me. I wanted to do Aldmeri Dominion and I didn't realize my alliance was something else. This is why I could never find the "Hooded Figure".

A bit more info:
There's actually 2 'main' quest lines, although only one is called that in your quest log (press J on pc). The one called main is given or rather started by the hooded figure. The other one, which kind of runs concurrently with the main is given at the starting zone after you get there via the hooded figure. These quests used to pretty much need to be done at the same time, although that is no longer so.

The quest marked 'main' will introduce you to the prophet, and will take you down a long, dark road filled with...well, you'll see. It is similar or identical for all players, regardless of alliance. The other one is your faction's quest line. This one takes you through your faction's struggle in the vast wars between factions, and is very different from one faction to another.

Both quest lines are <b>essential</b> for the full experience, and will give you tons of experience, a metric boatload (non-metric for US players) of more or less valuable gear and quite a few skill points. However, neither quest line is <b>required</b>, but you will miss out on a LOT if you don't do them. That being said, I strongly recommend against trying to run one from start to end all in a row, and would actually suggest a little more focus on the faction one, as having that done or near done when you finish the main line will be helpful.

As the faction quest line sends you hither and yon across Nirn, you will come to various villages, towns and cities. Initially the map symbol for these will be dark, and you need to do quests in that area to complete it. While not required, again you'll get well rewarded for completing them.

Here's a resource or two:
Possibly the most overall useful resource in general that I've found: http://en.uesp.net/wiki/Online:Online Beware, delve too deep at the risk of spoilers.

Buying, selling trading: https://us.tamrieltradecentre.com/pc/Trade/Search Not all that much help to start, but you will for sure need it later.

PC ONLY: https://minion.mmoui.com/ - Awesome add-on manager and http://www.esoui.com/addons.php - the location of the add-ons.

Don't be afraid to ask for help/opinions in zone chat (use /z <enter> to speak) and seriously look into joining some guilds (up to 5, many types of guilds available), but above all, have fun!