No need to go down the pathway of buying an expensive new bike... You can buy an aluminum bike such as a CAAD5 in your size (or any aluminum road bike built in the last 15 years) for under $500 that will keep you going for days. Road biking is a bit unnerving to get into if you've never ridden a road bike before. For one they tend to weigh less than the average mountain bike/commuter and they're thinner to boot.
The price of a good helmet is the next thing in line spending anything up to $100 and getting a floor pump and learning how to fill your tyres. The first few times most newbies will deflae their tyres back to zero and have to go through at least 200 strokes to get back to full riding pressure of 100psi
However learning to fill your tyres with air is a skill that you will need to learn at the very least... Add how to patch a tyre/tube and how to replace a tyre as you progress as well as how to remove and fit a chain. That is your bare minimum bike skills you will need to ride on the road proficiently over time. Next is getting a tool kit for your bike so you can do that on the side of the road.
Just take it easy is a good point of advice if you've been off the bike for a number of years. You may fall/crash so choose a good bike path in your area where if you have to fall off you can do it on grass, and choose an inexpensive bike so if you do fall you don't break it... No carbon bikes for first timers I'm afraid.
Ensure that your bike is fitted comfortably before you set off, at bare minimum you should be able to stand comfortably over the frame and you should be able to pedal proficiently without locking your legs at the furthest extension point between you on the seat and your cranks/pedals at full extension, and your legs should be perpendicular to the pedals when your feet are in the middle of the pedals to avoid knee damage, your arms should not be locked, and your shoulders should be neutral to your chest.
Go slow at first until you build your confidence, no death grips period on the bars, or on the brakes, and save any dare devil descents until you've done at least 500 to 1000km of riding as a newbie being off the bike for so long. Your strength will come from riding. My training regime for newbies is a standard 1 day on 1 day off at least for the first few months while slowly increasing the duration of your rides.
With a 1 on 1 off training regime and gradually increasing distance you should get in the ball park where you can do 50-100km within 2 to 3months if you train every other day and longer if you don't. Then its a matter of more complex interval training to work on your watts. You can get to anything with a consistent 3xx in it if you want to ride in your local grupetto or anything with a regular 4xx in it if you want to consider any sort of competitive club racing.
I'm going to be controversial and say I wouldn't bother with clipless pedals and for the most part based on statistics they don't save you any real waste of power either (there's no benefit to upstroke pedaling). Rather than wasting time on buying shiny new shoes get a tight fitting cycling jersey, usually one size smaller than what you would normally wear, and wear that. A good cycling jersey (and later an aero helmet) can make you up to 5km/hr quicker which is more than a new wheel set that will make the difference of about .8 of kilometer difference at best.
