Okay, so I haven't tried installing a wallet or buying BTC yet but following is what I learned…
Bytcoin is a cryptocurrency that doesn't actually exist. Nevertheless it still works, much like how many countries don't cover their paper money with gold but it still works. Its the trust in the value of currency that makes it usable.
First you need to get yourself a bitcoin wallet. Wallet can be stored on your mobile devices or computer in form of software, on your website account or on physical carrier hardware akin to USB flash keys.
Using wallet in form of software on mobile device or pc is most commonly used, as I understand it. Gives nice balance between security, privacy and ease of use.
Next would be physical bitcoin carries. They are designed from the root, meaning they cannont be reprogrammed or hacked. They are not connect to internet so this option is most secure but carriers can be costly, if you are particulary short on money.
Last option is creating account on bitcoin website and storing your bitcoins here. This option offers most vulnerablities and is generally not recommended.
I like the option of using bitcoin wallet as software on pc the most so I will further elaborate on this. There are few things that are good to take notice of when choosing this type of wallet.
-Wallet should give you full control over your bitcoins on it, meaning nobody else can freeze them or reverse transactions. To my understanding, there should be a possibility of reversing bitcoin transfers. It seems this is the reason why fees are being used and payment verification delay exists. Also generaly, you often get warned to do the business with trustworthy people and look for signs of scams like oddly low fees.
-Next you want the highest level of validation as you can get. You can get wallets with "full nodes" which work independently without third parties(most secure) but require 100 GB space. You can also get wallets partially dependent on third parties(less secure but I'd guess it is more lightweight too) or you can get wallet with centralized validation, fully depending on third party(meaning you gotta make sure that they are trustworthy).
-Wallets also differ the way their software is built. Bitcoin Knots and Bitcoin Core and some others are said to be open source and build deterministicaly which apparently means greater degree of transparency. Next there are wallets also open source but not build deterministicaly and lastly wallets using remote app which again depend entirely on third party. Open source is good because you can ask people understanding the code to verify if its legit wallet or whatever…
-Next is security. Most wallets don't support 2 step verifycation(using both pc and mobile device) except for Electrum wallet. 2 step verifycation can be compensated by using offline storage of wallet which is disconnected from internet like does Armory wallet.