Then i would suggest that you have a trading stack on an exchange (e.g. binance) and write a small program which does buy/sell depending on your logic via binance's API.

Exchanges are trading platforms. You buy or sell Bitcoin for other currencies (exchanging BTC, essentially). Think Forex (foreign exchange) for cryptocurrency. You'd get far better rates at most exchanges than Shapeshift, but at the sacrifice of time and convenience. Probably also not friendly to your ML scripts.

What is "most suitable"?

Since you're on Coinbase already - check out GDAX. It might do what you need at better rates than Shapeshift. GDAX is an exchange.

Since you are new to bitcoin: If you don't own the private keys, you don't own the BTC.
You are relying on a company to give you BTC when you want to withdraw. If they lose the keys through an incident, you are out of luck.
I'd suggest you take a look at all the wallets which exist, and choose one which does allow you to store the private keys.

Now, back to topic.
You don't need a node on your PC to use shapeshift.
But to use it automatically you need to write a small program/script which will (1) handle your private keys to create/sign transaction to shapeshift and (2) will query shapeshifts API to get deposit addresses.

Is there a specific reason you want to automate this via shapeshift? Exchanging coins via exchanges is way cheaper and more reliable/trustworthy.
Most exchanges do have an API. So anything regarding trading/deposit/withdraw can be programmed.