Get some combo platform/SPD Shimano pedals, online. Nothing special there. They're the SPD model that looks like it has a little additional rectangle around it. It gives a little extra if commuting or learning to ride.
Shoes to match. Probably go with a mtb or cyclocross style shoe at first. They have a walking tread. If you aren't racing or in the A-group, the weight penalty of a good walkable shoe that doesn't collect as much trash in the cleat is nice. I still own a pair.
The bibs/shorts. I'm a bib fan, the ones with suspenders. I find that some shorts only tend to dig into your waist to avoid slipping down. The suspender style holds itself up. I find that a good LBS will carry nice bibs and the REI style places carry generic stuff that isn't as good. I own some REI bibs, and they suck. The leg grippers are so loose I can fit my finger under them, the pad has gotten really thin over time, and it's not aging well.
Lights. Go ahead and make sure you have at least a good $50 or so red rear flashing light. If you ever plan to ride in lower light conditions, a solid $50+ front light also.
Next, saddle bag. Get a decent one, the Specialized ones are good. The velcro on the cheap ones wears out too fast. Fill that saddle bag with a basic multi tool, two tire levers, and a tube. Next, get a compact pump or your CO2. And by the love of God, don't get a cheap clip on frame mounted one that's going to bounce off into riders in the middle of a group ride. Either a CO2 in the saddle bag OR the compact hand pump in a jersey pocket. IMHO, the poorly mounted frame pump is super dangerous and a "spot a Fred" kind of thing.
Another comfort item for learning.........decent fingerless padded gloves. I don't wear them now, I should, but I've done enough miles that I'm not bothered any longer by the beating. Just learning, you'll appreciate them. A LBS item like the shoes as you need to try it on.
Make sure you wear your sunglasses or clear eye wear, bugs or debris in the eyes can be painful and make you crash.
Your bike likely didn't come with bottle cages. Don't cheap out. Get something like the Specialized "rib cage" or something that holds it well. Not the cheap wire metal ones you can bend around. And get bottles you can drink through by just squeezing, not having to bite and pull a stopper. Sometimes Phil Gaimon gives them out free after a fondo if you pay shipping. I recommend either the Specialized bottles or the Camelbak Podiums.
Some folks ride just to ride and don't care about data. If you do want to track your rides your options are either the computer OR a mount for your phone. I went the phone-mount way when starting riding. I found the cheap ones to not hold it securely and dropped mine once. Then I had wound up buying two phone mounts totaling nearly $30 to $40. You're a 1/3 of the way to a $100 Elemnt Mini or Garmin Edge at that point. If you need turn by turn directions, that eats up a phone battery. Learn to memorize your routes. I own a computer with GPS and maps and don't use the map unless it is the first ever time taking a few turns I don't know about. Even then you could pop your phone out of your jersey pocket for 30 seconds and check, then move along.
Own a track (floor) pump? Need that.
Get a bottle o' lube. Research online your cleaning options. That's a wickedly tribal topic that causes lots of anger among forum users, so just research that on Google and make your own call.
You should be pretty close to comfortable and happy at that point.