From your clarification it sounds like he wants to be playing a front-line fighter, so perhaps it's best (and safest for his long term prospects) if he starts gaining levels as one.
That said, some options to give him more front-and-center time in the game:
Give him an opportunity to end the battle before it starts. For example, a group of enemy are crossing a rope bridge, and if he's thinking fast enough, he can cut the ends of the rope bridge, sending all the opponents to their watery demise. This allows him to be able to claim (or brag) about the time he took out a whole group of X by himself. You don't want to do this all the time, but every once in a while it's a nice morale booster for the rogue.
Something other than a combat-centered adventure. Make an adventure not about killing a bunch of whatevers that are threatening a town, but retrieving an object thats very well protected. Or breaking someone out of prison. Something where his rogue skills will be the difference between success and failure.
Role-playing, role-playing, role-playing. A rogue isn't just a guy who backstabs and disarms traps. He's a guy (or gal) who knows how to operate in the seedy underworld in a way other characters can't. Players have an item they want to sell? The rogue is the guy who can ask around and use his contacts to find someone willing to make the best offer (and not just the low-ball offer received from an established vendor). Looking to buy something? The rogue 'knows a guy'. Need to keep watch on someone in the city? The rogue can blend in as he follows the target around. And he's the one who can recruit an army of street urchins to help him out.
The key here, though, is that the player has to be willing to do the above, and not only be interested in disarming the traps so that he can get into combat. Most of the responsibility is on them to make the best of the role they've taken on.
Ask for Help
Unlike many video or computer games, tabletop games are expected to be social experiences. Creating a character without the help of a more experienced player (or preferably, your GM) is going to be frustrating. Your first option should be to ask the rest of the table for guidance.
If everyone at the table is new, consider asking online (like you are doing now). There are many excellent guides online that talk through the character creation process in more depth.
Failing either of these, you might go to your local game store for D&D organized play and ask someone there.
Carefully Read the Rules
All of the questions listed above can possibly be known by carefully reading the entire PHB. The entire first section of that book deals in character creation: races and classes are not all the choices you face. In particular, you seem to have missed the Backgrounds section which explains personality traits, bonds, and other things.
Compare Your Work To Others'
Look at other people's completed character sheets. You can search for pre-generated characters online and the 5E starter box comes with several. This would explain what goes in each cell or line on the character sheet.
The PHB also includes "Building Bruenor" as an example of creating a 5E character. Each section will mention the choices are involved with creating Bruenor and how they contribute to the character. Even as an experienced player, I found these boxes helpful my first time in 5E.
Do It Wrong
You will almost definitely make mistakes. Take this character into a game with more experienced players and let them correct you. Don't get discouraged. Treat it as a learning experience.
Best Answer
You're rightly confused — you don't normally get three attacks per round like that. By itself, fighting with two weapons gives you at most two attacks — one from the normal Attack Action and one from a Bonus Action with the off-hand weapon.
Vax therefore has something else going on that is allowing that third attack. From the Critical Role Wiki's FAQ:
So Vax is making the first two attacks according to the normal rules for Two-Weapon Fighting (on page 195 of the PHB), and then making a third via the extra Action granted by D&D 5e's version of the spell haste (p. 250).