After doing a little reading and talked to an old friend, I was told I should not use Coinbase especially to store my crypto since I don't have control over the keys.
I am just looking for clarification and recommendations on the following.
1) What would you recommend I use to store my BTC? I was thinking of looking for a program I can just run on my computer to store my crypto.
If you are looking to run a wallet on the computer then the best choice is 'Electrum'.
2) Do these wallet programs allow you to buy and sell BTC?
Nope! You can only purchase bitcoins on centralized exchange services like Coinbase or P2P platforms like LocalBitcoins. Since you are using Coinbase from long time, it is advisable that you continue doing so. But as soon as you purchase bitcoins on Coinbase, withdraw those to your Electrum wallet.
3) If I use a hardware wallet, cold wallet etc, how do I go about cashing out crypto? Do I have to use an Crypto Exchange? Are the fee's going to be similar no matter what I use?
Yes, you still need Crypto Exchange to sell your coins. If you are using cold storage then you first have to either import or sweet the private key in a non-custodial wallet like Electrum. Then you can send the coins to the Crypto Exchange using current network fees. Wallets like Electrum will show you 'recommended' network fees which will get your transaction confirmed within next few blocks. However, if you aren't in hurry, you can manually set lower fees and still get your transaction confirmed in few hours.
I am just looking for a better place to park my BTC. Coinbase fees for sending to another wallet are crazy high. I am hoping to avoid this if possible along with having a wallet that I control the keys to.
Currently there are high number of pending transactions in mempool so network fees is soaring. That's why Coinbase is taking benefit of the situation and charging arbitrarily higher fees. Using non-custodial wallets like Electrum, you have full control over keys and coins. You can sign and send transaction using your own preferred fees.
I have the ability to backup anything on my PC to external hard drives and to cloud storage.
If you are going for Electrum then make sure to backup mnemonic seed. I would suggest you to write seed on a physical paper than saving it on hard drive or a cloud storage.
Lastly, I was thinking of downloading the current BTC blockchain to an external drive. I had read that you get a wallet. I may be wrong. I am not certain how that all works. Any benefit of doing this other than mining?
Regards
The full size of BTC blockchain is 307 GB. I would only suggest you to run full node if you are intending to use it for an application purpose (in production). The wallet you are talking about is Bitcoin Core. No need to download the whole blockchain if you just intend to use Bitcoin Core for wallet purpose. Better go for SPV node which will only download block header and sync fast. However, it would be more appropriate if you use Electrum instead of Bitcoin Core since Electrum is more-friendly for new users.