Let's see ...
In Chapter 1, yeah, you can do most any mission in order and skip them if you want. We're recommending you do them in order here because you were originally asking what to do next. Finishing a mission puts you in the outpost where your next mission or primary quest is. So, if you've lost your way, you can find it again by doing the most recent mission and seeing where it leaves you.
Realize that "missions in order" refer to the storyline; they don't line up on the map. Especially in the Ascalon area, the missions jump you all over the map.
Ok next, armor and weapons. The max damage any sword will have is 15-22. The max damage any axe will have is 6-28. As a warrior, the max base armor you get is 80. All of this comes later in the game. Don't worry about it yet, you'll get there in time. The game is pretty good about giving you access (via monster drops and armor crafters) to gear sufficient for the area.
If you're alternating between a sword and an axe, are you doing it at the same time? As in, you have points in both axe and sword mastery, using both axe and sword attacks on your skill bar? If so, that's usually not a good idea. Most warrior builds stick to just one type of weapon. If using swords, no points are spent in axe mastery and no axe attack skills are carried.
As for strength, I personally think it's one of the most awesome aspects of warriors. So please don't let someone telling you it's useless dissuade you. When I'm playing as a low-level warrior, I usually try to get my sword/axe/hammer mastery up enough to meet my weapon's requirement. I spend the rest of the points in strength and tactics. The points you spend where varies a lot by what sort of skills you're using and what your main role in the team will be.
Can you come back and do quests later, after you're tougher? Yes, you can. The only part of GW that ever really shuts you out of finishing quests is the preSearing part. If you go through the Searing, you can't ever get that character back to preSearing nor can you ever finish pre quests. That won't happen to you anymore now that you're in postSearing.
You can even abandon quests and take them again later. Say a NPC named Snuggle Bunny gave you a quest called Save the Rabbits. In the process of saving the rabbits, all sorts of terribly big, nasty monsters spawn outside. Said big, nasty monsters being there in the map make it really hard for you to progress past this map. While in a town, you can select the Save the Rabbits quest in your quest log and hit the Abandon button. Then you can proceed to explore outside without that quest's monsters in your way. Later, when your character is bigger and stronger, you can come back to Snuggle Bunny and take the quest again. Then you can go outside and beat the crap out of the terribly big, nasty monsters.
Which are the quests you're having trouble with, out of curiosity? Realize also that while your character may be stronger later on, the henchmen available in outposts won't be. So if there's a quest giving you a lot of trouble and you want to save it for later, it's sometimes better to use heroes (if you have NF or GWEN) or even other real players.
Another couple tips, especially if you're mostly using henchmen, always try to bring a res signet or skill and some sort of self heal with you. It's good practice in GW to always try to bring one of each. Warrior's get the Healing Signet skill, which should be just fine. The next tip is to give the henchmen time to recover between fights where possible. As a warrior, you have a max of 20 energy. Your henchmen monks and elems have a lot more. They don't manage their energy very well, so they often run out during fights. After dealing with a group, give the henchies a few seconds to recover before charging the next group.
(I realize the temptation of full adrenalin charges is very strong, I've played warrior. But if you're finding your team having an increasingly hard time killing each next group then you may be going too fast.)