The basic Fighting Style features seem reasonably powerful as second-level abilities, and the Hunter archetype has a lot of options that are quite strong (with Colossus Slayer probably being an easy favorite, and Escape the Horde being nice for combat mobility). The spells are pretty good too — it's easy to escape notice, but a minor version of Arcane Archer is basically rolled into 5e Ranger, with ranger-only spells Hail of Thorns and Lightning Arrow (and Cordon of Arrows, Conjure Barrage, and Conjure Volley too).
The exploration and tracking utility features are decent, especially with a communicative / cooperative DM where they actually match the campaign — and double-especially in a game with a lot of exploration and travel. (Although for skills and general helpful magic, it's kind of hard to keep up with the bard — I'm kind of tempted to ask a "Are 5e Bards kind of overpowered?" question.)
So, back to the archetypes.... I think that Hunter isn't underpowered. That brings us to the Beast Master archetype, and to Does the Ranger's Companion synergize with the Ranger?. I think, as Joshua says, the quick consensus seems to be that it's kind of weak in comparison, at least in terms of sheer combat power. But, one could also consider the companion as a non-combat helper, and in that case, as a DM, I would have no problem ruling the companion's training and ability to communicate with you as significantly higher than what you could get by buying or raising a pet with the animal handling skill and no class feature. Scout for something in specific; fly overhead and look for danger; fetch items that a normal animal couldn't distinguish; basically do anything out of combat that isn't completely unreasonable. Or, closer to combat, I'd let you not be surprised when your (nearby) companion isn't, for example.
If you're looking for combat, Panther and Wolf are probably the best Player's Handbook options, and I'd be strongly inclined to support the "attacking companions keep doing that without needing more instruction" house rule mxyzplk offers in the does it synergize? question. Particularly, I'd have a hard time explaining that the companion can't do that but that if you went to an animal trainer and bought an attack dog, it could. (Insert boring metagame discussion about NPCs taking XP.)
And I might also house rule a higher minimum hit point rule, because as a DM, the other alternative is really to have combat opponents mostly decide to not target the companion, which could feel inauthentic. I have a suspicion that the current "4× ranger level" minimum doesn't scale appropriately, but I haven't actually seen it in action. Likewise, you add your proficiency bonus to saving throws the companion is proficient in — but I don't think any beasts are proficient in any saves, so that's moot in practice. I think adding a little more protection here is warranted (maybe half proficiency to all saves?).
Also, there's currently no mention of the companion using hit dice to recuperate with a short rest, but I would certainly also allow that, and provide more dice with ranger levels to keep up with the party. (Mike Mearls notes on twitter that the companions can use hit dice like characters, but doesn't address scaling — 15th level characters have 15 hit dice, but the poor companion is stuck with the initial one or two.)
Since the consensus seems to be pretty much that the Beast Master is a weaker choice, I think most game tables would be okay with these rules. But if not, you might want to consider focusing on the Help action (at 7th level, the ranger can give this instruction as a bonus action). (Maybe combine this with a companion like the owl for flyby help without staying in range or provoking attacks of opportunity.)
Also, as the game expands and your ranger travels to more exotic locales (or can justify having been in them as part of the backstory and the DM is good with that), dinosaurs and giant insects (and crabs!) increase the power over the Player's Handbook beasts.