Here's what you're trading for the alertness feat if you don't take the abil score upgrade and instead take the feat:
- +1 to damage
- +1 to hit
- +1 to AC
- +1 to Dex saves
- +1 to Dex checks
- +1 to init
The question then, ultimately, becomes, is +5 init (net +4), no surprise and no advantage on attacks against from hidden opponents worth it.
The latter two features are very dependent on your campaign and DM. Surprise should be a fairly frequent occurrence on both sides of combat, but that still depends on how willing your DM is to allow it or stage his monsters to have them obtain it (and kind of how cautious your group tends to be). Monsters attacking from hidden is another one that really depends on your DM, you group and how well you guys are at nosing out monsters from the shadows.
So ignoring those two items since they are DM and campaign dependent (and thus can't be weighted objectively), the question then becomes, is +1 to Dex more or less beneficial over 4 levels than +5 to init.
For pretty much any character other than the Assassin Rogue, I'd probably argue that they should take the stat upgrade early, the feat at L8 and then the last stat upgrade. However +5 init has amazing synergy with the Assassin Rogue and you're going to get a ton of mileage out of it.
If you're already at 20 Dex (if you managed to start at 20, or 18 and are at L8), then there really isn't any stat upgrade that is worth taking over this feat (though there may be better feats). Rogues are skill monkeys, yes, but +5% in a single ability set of skills is not worth the +25% to initiative and other features o this feat. The only one that would be worth considering at all is Con for the extra HP, but it's really not that many and you're better of boosting your damage significantly.
Take the feat at L4 (or even better, play a human and take it at L1).
This is really strong, at least for certain builds. Anyone who wanted to focus on Str anyway is likely to end up playing this race.
Firstly, Barbarians. Barbarians are currently one of the most MAD classes in 5e, needing good Str, good Con, and at least reasonable Dex. Your race would allow them to dump Dex and just focus on Str and Con.
Secondly, Druids. This is probably the worst case - your proposed race gives a Moon Druid an incredible boost to their Wild Shape forms. Str and Con are the strong points, and AC is the weak point, of most beasts, especially the ones Druids like to Wild Shape into.
Next, Fighters. This is the least problematic, since a Fighter could already afford to focus solely on Str and Con, but it does mean they end up with a better AC than they otherwise would have.
Oddly enough, it also enables Str-based Monk and Rogue builds. This isn't really a problem though, since in many ways Dex is inherently stronger than Str anyway.
Comparing it to Monk isn't really that useful, since they're essentially the same, but anyway:
Level 1: Typical Monk has 16 Dex and 16 Wis, giving them an AC of 16. A Barbarian of your proposed race has 17 Con and 15 Str, giving them an AC of 15, or 17 with a shield.
Level 4: Typical Monk has 18 Dex and 16 Wis, giving them an AC of 17. A Barbarian of your proposed race has 18 Con and 16 Str, giving them an AC of 17, or 19 with a shield.
Level 8: Typical Monk has 20 Dex and 16 Wis, giving them an AC of 18. A Barbarian of your proposed race has 18 Con and 18 Str, giving them an AC of 18, or 20 with a shield.
Level 12: Typical Monk has 20 Dex and 18 Wis, giving them an AC of 19. A Barbarian of your proposed race has 18 Con and 20 Str, giving them an AC of 19, or 21 with a shield.
Level 16: Typical Monk has 20 Dex and 20 Wis, giving them an AC of 20. A Barbarian of your proposed race has 20 Con and 20 Str, giving them an AC of 20, or 22 with a shield.
Your proposed race can always have a better AC than a Monk of the same level if they choose, despite the inherent weakness of starting with +2 in a single stat rather than +1 in two stats.
You're right that basing it off Dex and Con would be even stronger, but only because Dex is inherently stronger than Str. Your footnote about bonuses, however, is less accurate. A minor bonus to AC, while good for everyone, is hardly a game-changer. Your proposed feature, on the other hand, can form the foundation of a build. It replaces a core feature of the Barbarian or Monk, and is effectively completely free, especially since your proposed race has fire resistance on top of it.
Best Answer
You understand the way to boost ability scores correctly
At the beginning, when you make a character, you apply the ability score boost due to race after you have assigned the numbers to each of the six abilities.
When Ability Score Improvement(ASI) comes at 4th level, 8th level, (and 6th level for Fighters) and so on, you can apply two points to any ability score at that time when you have gained 4, 8, (etc) levels in a class.
As an example, a human barbarian
On page 49 of the Players Handbook, the Barbarian class feature of Ability Score Improvement tells you that you can at levels 4, 8, 12, 16, and 19 increase one ability score by two points, or two scores by one, and none may be increased beyond 20. Each class has an entry for ASI, so the player needs to read the ASI entry for their class. (It's different for Fighter, for example.) Let's say that our Barbarian was a human who rolled the following raw scores for abilities.
Str 15 Dex 11 Con 14 Int 10 Wis 11 Cha 10
A human gets to add one to each ability score.(The racial boost you use at character creation).
Str 16 Dex 12 Con 15 Int 11 Wis 12 Cha 11
At 4th level, the barbarian gets to add two points(ASI).
Either add two to one score, or add one to two scores.
Examples of making that choice:
Str 18 Dex 12 Con 15 Int 11 Wis 12 Cha 11 (+2 to Str)
Str 16 Dex 12 Con 16 Int 11 Wis 12 Cha 12 (+1 each to Con and Cha)
If any of your players wish to multiclass, ASI is based on class level, not total character level.
For example: a third level Barbarian who chose a level in Fighter when enough experience points were earned for 4th level (2700 XP, p. 15, PHB, table) would not get an ASI, being Barbarian (3) Fighter (1). He would need to earn 4th level in either barbarian or fighter before getting an ASI.