I'll start out by saying that I generally prefer at-will Wild Shape to Daily Wild Shape, even if you have daily uses of certain forms with an otherwise at-will Wild Shape. That said, this version of Daily Wild Shape is much better designed than 3.x edition, and it's something that I could suck up and happily play a Druid. Getting Wild Shape at first level is ESSENTIAL since that's such a huge part of the class's identity. Most of the time if I play a Druid, it's because I want to play a shapeshifter. While you only start out with one use per day, the Circle of the Moon (the circle that focuses on shapeshifting) grants you an extra use per day, and at second level you're already up to a baseline of 2 uses (3 with Circle of the Moon). Considering the duration (level + Con mod HOURS) you can conceivably spend most of any day shapeshifted even at low levels.
Speaking of Circles, I actually really like that Druids have the option to either increase their spellcasting ability (with Circle of the Oak) or go with a bigger focus on Wild Shape (with the aforementioned Circle of the Moon). In addition to an extra use of Wild Shape, Circle of the Moon gives you a small amount of healing when you revert back to your natural form and provides access to new forms. These are the combat forms, so basically if you're not Circle of the Moon your Wild Shape is mostly for utility, as even your starting Shape of the Hound isn't very good in a fight (its advantages are a high speed and great senses).
The biggest problem for me is that even with Circle of the Moon your different forms don't scale. So you start out with Shape of the Bear, but at 3rd level when you gain Shape of the Great Cat it doesn't make much sense to use the Bear anymore; the cat gets a lower base damage, but if you pounce you make two attacks, and if both hit you knock the target prone and bite them. Both shapes get the same AC. A better design would be to have a handful of different scaling forms that filled different niches. So you'd have Shape of the Bear for when you want to be durable with decent damage (it would have higher AC, and perhaps some kind of damage reduction or temporary HP mechanic), and Shape of the Great Cat would give you mobility and spike damage. You could even buff up Shape of the Hound with some sort of "pack attack" mechanic (low damage and AC, but it gives your allies Advantage as it harries the enemy).
Point being, part of the fun of having multiple forms that you can turn into is getting to make meaningful tactical decisions regarding which form you decide to take. It's a bit dull if you have a highest-level form that becomes a no-brainer to use whenever a combat breaks out.
The utility forms (those available to all Druids) look good. You've got all the basics covered; hound for speed and improving your senses, rodent for hiding and climbing, fish for swimming and breathing underwater, steed for even more speed and carrying capacity, and bird for flying. You end up having access to all of your bag of tricks by 6th level, too (with the bird). My only concern would be that perhaps 6th level is too early to have access to such a reliable form of flight (Circle of the Moon Druids can use Wild Shape 4x/day by that point). Given that the duration of Wild Shape is so long and that even Circle of the Moon Druids will want to spend at least one battle in their natural form to sling spells around, most will be planning on using a utility form at least once each day. Granted I LIKE that you can use Wild Shape often enough, early enough for these non-combat utility forms to see play (despite Wild Shape not being at-will); the issue is potentially how early you gain access to flight. Consider that Circle of Oak Druids won't be using Wild Shape for fighting anyways, and you could easily run into situations where they're flying up to a safe perch and raining death on their enemies without fear of reprisal.
Finally, Shape of the Dire Beast needs a simple fix. Size should not increase to Huge, at least not in all cases. All of the Druid's combat-worthy forms are already Large sized, and by increasing them they can't fit through your standard door. I mean, a lot of big cats would be at the small end of Large anyways, if not outright Medium, so it makes more sense to me for a dire version to be either solidly Large, or at the bigger end of Large, but NOT Huge. Shape of the Dire Beast is what allows shapeshifter Druids to keep up with the scaling of the melee classes, and it doesn't make sense to deny them their basic functionality just because the DM set his adventure in cramped spaces.
Another concern I have is that you seem to give up more by going Circle of Oak. I mean, you pretty much have no combat utility from Wild Shape (well, you certainly won't be keeping up with the melee classes), but Circle of the Moon Druids can still use spells to full effect. It's just that Circle of Oak Druids get to recover expended spell slots (like the other "full casters") and they have a list of automatically prepared spells.
Cantrips are decent enough, though Druidcraft and Spare From Dying are notably missing. Shillelagh is a solid enough melee option; you won't deal as much damage as the dedicated melee types, but the 10 foot reach is a nice perk. Fire Seeds is pretty low damage but looks to be a good "finishing move" option, especially considering the fact that you get two low-damage attacks. Faerie Fire is surprisingly nice; sure, you give up making an attack, but you can cause enemies in a pretty big area to grant Advantage. This might see a lot of use.
At first level, Entangle was always one of my favorite spells, and it has some serious teeth. Its area is pretty small, but the combination of decent damage and a solid mobility-debuff looks like great fun. Thunderwave was also a happy surprise to see on the Druid's list. Great area effect with the potential for pushing enemies off of cliffs. These two offensive spells are likely to see a lot of use. The utility and healing spells that round out the list are pretty much to be expected.
I won't go into much detail past this point, but incarnations of Web, Hold Person, and Flaming Sphere look nice; very well done. Flame Blade is a neat "haha, I can deal solid melee damage plus I'm good if you come across any trolls!" option, and Heat Metal might not have the duration of previous incarnations, but the disarm if cast on a weapon vs disadvantage if cast on armor riders seem interesting enough.
The lack of Summon Nature's Ally is immediately noticeable; I assume they want to get a better handle on core mechanics before they muddy the waters with summoning (which is notorious for balance issues).
EDIT: Added concerns about Shape of the Dire Beast.