Revised Ranger Druid build

I'm building a new character. I like being a full spellcaster, I like archery, and I like the idea of having a beast companion. My primary hesitation about Wild Shape is that you can't cast spells (until high level), and I like casting spells. I have not played Druid or Ranger before.

What are your suggestions as to which or what multiclass combination to play?

Note that I am looking at the UA Revised Ranger, Beast Conclave, not the PHB Ranger. UA Druid stuff is an option, too, as is possibly a homebrew option.

Furthermore, I need to select a race. All races from PHB, Volo's, Tortles, etc., are all allowed, and the associated ASIs can be freely changed from ability to ability: I could make a +2 Wis, +1 Dex Dragonborn if I wanted, for example.

Just a word of caution - Mike Mearls has said before that the UA classes haven't gone through a multiclassing balance pass. The UA Ranger, IMO, is a good example of that. It gives a lot of features at 1st level, and the beast advancement is based off proficiency which is based on your entire level, so you still get to advance your biggest class benefit while taking levels of another class.

Ok, now that's been said we can move on. You mention archery and casting, and were worried about wild shape blocking casting. Sounds like any of the druid options except Moon Druid - wildshape in combat would prevent both casting and archery.

My first through would be a Circle of the Shepard, from the Druid UA. Specifically a Hawk Spirit Bond can give you (and allies) advantage on ranged attacks to bolster your archery while still giving full casting. Only for 1 minute, but a bonus action to start and recharges with a short rest. Also full beast speech plays well into the ranger beast conclave. Finally it grants bonuses with summoning, which can act as both additional meatshields for archery or coordinate with your beast companion.

This gives you a good spell efficiency - one summons early in a combat then supported by archery and your beast companion means you have a lot of spell slots not needed for just combat support but rather you can do whatever you want with them. Combine with a scouting wildshape and you've really got someone who can cover both the exploration and combat pillars very well.

With the ability to change which ability scores are boosted, I wouldn't worry so much about race. Go for whatever makes the character the most interesting to run. Sure, some racial features might give you a bit of an edge, but I wouldn't worry about it too much considering what you'll have between wildshape, casting and ranger abilities that you've got so much covered. Maybe Eladrin for Misty Step in you get closed on in combat.