I didn't participate in any previous "panic" so I wouldn't know.
But giving people a bonus for going first and making it easier to go first synergies really well. And at 1st level, going first can win fights: dropping an enemy and negating damage before it even gets a turn. That's strong in and of itself, but adding the ability to just outright ignore any and all difficult terrain is really good on top of that.
I'd replace advantage with adding proficiency to initiative. The end game bonus is higher, but that comes into play far later, when the alpha strike is less devastating. The low levels it is weaker, thus making it more in line with other first level features.
I'd also move the difficult terrain avoidance back up to higher level. Just too good.
Give the ranger a small skill bonus instead. An expertise variant, perhaps limited to survival or perception. Something that doesn't directly help kill things...
How exactly does going first win a fight? It give you an advantage, sure, but there is a good chance the Ranger with a high Dex was going to go first anyway! He get's one shot with advantage with his bow, which again might have hit anyway, and now his ability is done. If he's melee there is no guarantee that an enemy will be in range to attack, so that wastes that ability. That's it for that combat.
How is that so great again? It's cool, sure. Get jumped by some goblins and the Ranger reacts quickly and efficiently. That sounds like a Ranger to me. But the other side being down one goblin isn't going to end any encounters.
The Ranger needs
something that is useful at 1st level to help him keep up with the other classes. Barbarians get 2 Rages that gives them +2 damage, resistance to all physical attacks and advantage on all strength checks. Paladins get a combat heal (that increases every level) that can also cure any disease or poison. Fighters get a self combat heal usable every short rest plus a Fighting Style that adds either +2 to ranged attacks, +2 to one-handed damage, re-rolls on two-handed damage (essentially advantage on damage rolls), etc.
Meanwhile the PHB Ranger got exactly nothing combat related. Adding advantage to initiative rolls, advantage to the first round of attacks (one or two depending on level) and a situational +2 damage has to stack up against everything that the other classes get. Compared to the Barbarian's Rage, it's not looking that overpowering. Ignoring difficult terrain is nice, but it doesn't happen all the time. Honestly in the canned adventures that I have played it probably comes up less than 10% of the time. Useful, and great flavor for a Ranger, but hardly game breaking, even at 1st level.
By 6th level the Revised Ranger's situational +2 bonus goes to +4 and they can make it slightly less situational. Meanwhile the Barbarian can Rage 4 times a day making their bonus almost an 'always active' ability. The Paladin can now drop a 30 point heal and the Fighter (most likely) gets an additional +1 to hit and damage (maybe AC too) from his ASI and his self heal goes from 1d10+1 to 1d10+6.
Of course there are a lot of other factors for each level of all of the classes.
The paladin's spells directly translate to higher personal damage, due to the smite. New spells mean more damage when needed. And each level has a smite spell for extra utility.
The ranger doesn't have that. They can just cast hunter's mark for longer (and lose it when they get hit, since they're not proficient with Con saves). Their damage stays constant.
At the very best, this is true until 17th level when they can cast swift quiver, which is useful for archers and useless for two-weapon fighters. And comes at the cost of hunter's mark.
However, two weapon ranger has the same DPR at level 20 as at level 12. Even the archetype features are defensive.
Ranger spells are already pretty problematic.
First, the archetypal rangers (Robin Hood, Drizzt, Strider, Tanis Half-elven, Belkar Bitterleaf) are not spellcasters. Spells should be optional. Spells should be a secondary decision point. Like how warlocks pick a patron and a pact bond.
Second, nothing draws attention to the "class feature" spell (hunter's mark). You need to read far deeper than a casual glance at the class (the back of the book) to find that. All rangers should just get that for free, drawing eyes to the spell. If it could be buffed in the class, that would also be cool.
Drizzt used magic all the time, Faerie Fire and Darkness immediately come to mind. Although those were Drow spells. Honestly Salvator was horrible at representing magic in his novels. I have only read a few but I remember him describing his characters resting for months to recover from some battle or other and I'm thinking, "Why the heck don't they just cast a few heal spells?" It was pretty frustrating to read honestly.
My favorite Ranger from D&D novels was The Justicar (real name Evelyn) from the Greyhawk Classics series. He is a huge, bald-headed, death machine that used ambush, dirty fighting and well placed spells to take out his enemies in a ruthless and efficient manner. Much to the chagrin of Benelux, his sentient bastard sword, that was more used to dealing with honorable paladins. He also pretty commonly used healing magic, because why wouldn't you?
But more on point... Yes, the Ranger spell list could use a boost. But you left out a few good spells in there. I don't have my books, but Lightning Arrow is a good one. Definitely need more melee spells though.
