Is periodically transferring Bitcoin from an exchange to a private wallet cost effective? I'm new to this, I've read a lot about it and I've decided to start saving money on Bitcoin by buying a fixed amount every month.
I know it is safer to store my Bitcoin on a private wallet instead of having it on the exchange I'll use to buy. But I know that moving it from the exchange to the wallet will incur a blockchain fee.
It feels to my that by moving Bitcoin to my private wallet each month I'll be constantly paying and would be cheaper to just store it on the exchange.
What are your thoughts on this? What's the must cost effective way of moving it to my wallet? Will doing this once a month be as costly as doing it in larger amounts once a year?
I'm looking to hold for a long time.
Any advice will be much appreciated. Best.
PS: I've done my research before asking here but couldn't find a good answer.
But I know that moving it from the exchange to the wallet will incur a blockchain fee

There is a fee involved in all bitcoin transactions which goes to miners. However, withdrawal fees of most of the exchanges are not same as the fee used in bitcoin transaction for withdrawal. Most of these exchanges have fixed withdrawal fee like 0.005 BTC on Binance. Some don't have withdrawal fees like FTX (Maybe promotion and won't be free forever). Some exchanges allow you to set your own fee like Bitmex (Minimum fee changes according to mempool)
Spot exchanges also have their own fee structure for withdrawals. Peer to Peer exchange like HodlHodl uses 2 of 3 multisig so fees work differently and you don't keep bitcoin on exchange ever: https://hodlhodl.com/pages/faq

What's the must cost effective way of moving it to my wallet?

There are different types of fees involved in exchanges. You will have to explore all options and see what works best for you. Also prefer using an exchange that supports withdrawal to segwit addresses, LN and Liquid. Layer 2 solutions have lower fees compared to on-chain transactions most of the times.
I am going to make a list of exchanges that support latest bitcoin technologies soon. Until then this link can be helpful for exchanges that support LN: https://ln.guide/docs/EXCHANGES.html