New to D&D, a little unsure about character creation stats

Question

So, I just recently started playing D&D5e a few days ago. I have created my own character but I'm a bit confused about how certain stats are calculated, and what path to go down with my character. The character I rolled is as follows:

Race: Tabaxi

Class: fighter

background: I wasn't aware of this mechanic when I created my character, so I just assumed it meant to write a backstory for my character. Being a swordsmith, I can't really find any official backgrounds that works with my backstory (monk/cenobite turned swordsmith due to drama). So I'm a bit lost on this front, and I don't know how important it is.

stats:

STR: 19 (+4)

DEX: 16 (+3) Dex rolled as 14 but Tabaxi gain +2 to dex

CON: 15 (+2)

INT: 14 (+2)

WIS: 12 (+1)

CHA: 08 (-1) Cha rolled as 7 but Tabaxi gain +1 to cha

Have I calculated these correctly? I found a few conflicting articles when creating my character, so I'm not sure I added the racial bonuses or stat modifiers correctly.

My skills are Arcana, Athletics, History, and Survival.

Answer 1

Ability Scores

Your ability scores can't be right - without a racial bonus (or a feat as a Variant Human), there is no way for an ability score to be 19 as a starting character.

Saving Throws

It appears you've conflated saving throw proficiency with stat bonuses. Being proficient in a type of save does not increase your stat at all times, it only adds your proficiency bonus when an effect forces you to make a save of the type matching the stat.

Backgrounds

Backgrounds are important mechanically, at least for determining starting proficiencies - each background provide two skill proficiencies, plus a combination of any two language proficiencies and tool proficiencies.

They also provide a background ability (Acolytes can get free spellcasting, Soldiers have some reputation from their battle prowess, etc). Some of them are more potent than others, but all have their uses.

As for your desired background, there are quite a few appropriate choices in the PHB. Acolyte or Hermit would work if the monk part is more important, while Guild Artisan would work for the weaponsmith part. Note that it is also permissible to adjust the backgrounds, as long as you take two skill proficiencies and two tool or language proficiencies.

Skill Proficiencies

At the very minimum, a character should have four - two from class and two from background. Some races gives extra, and some classes let you pick more than two.

As a Tabaxi, you should have six - Stealth and Perception from the race, two from your background, and two from Fighter.

Armor

Heavy armor gives you a static AC; your ability scores do not affect it. Chainmail, for instance, is always an AC of 16. A shield would bump it to 18, and better armor could be even higher.

That said, your proficiency bonus is not added to AC by default. There may be feats or class abilities that can temporarily apply it, but it's not a full-time thing and certainly not at 1st level.

Commentary

While creating characters is a decent exercise, and gives you cause to write questions like this, it can only be safely undertaken as a thought exercise. Almost all DMs who use rolled stats will want to have them rolled where they can see, while many use point buy instead. There may also be setting-specific cultural elements (or even mechanical world design elements) that influence race and class combinations.

Answer 2

Welcome to Stack, and tabletop gaming! You do have a few glaring issues in your character, which I'll do my best to help with.

Background

Background is not something freeform that you write yourself. I mean, I guess you could do that, but you will be losing several important increases to your character and playing an overall less powerful character if you do.

The backgrounds given in the rulebooks also provide your character with proficiency, specific roleplay opportunities, and sometimes even new abilities. Point being, they give a mechanical advantage as well, not just a general backstory for your character.

To address the concern of your character's Background not matching their personal history, that's something you can chat about with your DM. Your DM should be flexible on what the Background actually entails for your character's history, and I've never met one that strictly expected people to play a literal textbook version of their character's personality.

Stats

Something is off, as you have a starting strength of 19, which should not be possible under any method as a Tabaxi. The absolute highest you could have is 18 if using the dice roll method.

If you did use the roll method (your post is unclear, but you mention that a stat "rolled" as something multiple times), unless you were given permission by your DM, they will want the dice rolled in front of them, not on your own, to prevent cheesing/cheating.

Saving Throws

Saving throw proficiency does not add your proficiency bonus to any rolls for that stat. It only adds proficiency to those saving throws. All other rolls are unaffected by proficiency to saving throws.

Skills

Something is off here as well; you don't have as many proficiency as you should, and you have one that isn't possible for you to have. When creating your character, you get skill proficiency from three sources:

Class. When creating a Fighter, you can pick two from Acrobatics, Animal Handling, Athletics, History, Insight, Intimidation, Perception, and Survival.

Race. Being Tabaxi gives you proficiency in the Perception and Stealth skills.

Background. You didn't pick one, so you don't have those. This is another reason why Background is important beyond the character's history, and why it is necessary to select one.

Arcana is not an option for you (though it could be, depending on Background), so you have no way to have selected that Skill. Additionally, you should always have Perception and Stealth as a Tabaxi racial, and you have neither.

Armor

Armor does not apply your proficiency bonus to it. Proficiency in armor simply allows you to wear it.

"10 + Dex bonus" only applies to being nude or wearing regular clothing; it does not work if you are wearing any armor.

How your AC is calculated depends on which armor type you are wearing. Light armor is the armor AC + dexterity bonus. Medium armor is Armor AC + dexterity bonus (max of +2). Heavy armor is simply Armor AC, no bonus from dexterity.

In your given example, if given Plate armor and a shield, your character would be at 20 AC. 18 base AC from the armor, gains +2 from wielding a shield as well. You would, additionally, have disadvantage on all Stealth rolls, so that may or may not be worth it to you or how you want to play your character.

Is your AC a bit high with Plate as a level 1? Perhaps; but that is why it isn't possible to start with it. You would have to earn it in game somehow, and overall, it isn't absurdly high. Yes, you're hard to hit if you gear yourself as the tanky type, which is exactly how it should be. It wouldn't be fun to be the tanky armor wearing type if you were easy to hit!