How often put bitcoin in cold wallet

So I’m new to bitcoin and have about $500 worth of btc so far. I just started this month and I’m trying to do regular purchases of $50-$100 once a week.

I just got my cold wallet delivered last night and I’m gonna set it up today. My question is, how often should I pull my btc off of the exchange and store it in the cold wallet? I understand to withdrawal the btc I’ll pay a small fee. Is this a percentage or a one time fee. Currently I’m using Coinbase but it is quite expensive so I may switch to strike or kracken once I do some more research. I guess I’m just asking regardless of what specific exchange is being used.

Should I immediately pull my btc off of the exchange or wait until I have $1000 or so? What is the most efficient and safest way to do this.

My goal is to continue investing to accumulate.1-.2 btc as my first goal so I won’t be selling/trading at all for a long while if ever. I’m also hoping to have tens of thousands invested over the years so I am not too worried about $50 being locked up for a month or anything like that.