If you are experiencing issues or you need more info, feel free to reach out to the community. You can find the CLI team at #monero or #monero-dev, or else check out the Hangouts page for a more complete list of contacts and chatrooms
Use a @remote-node while downloading the blockchain locally, this will allow you to use Monero immediately and switch to your local node once it's completely synced
You are strongly advised to verify the hashes of the archive you downloaded. This will confirm that the files you downloaded perfectly match the files uploaded by the Monero development workgroup. Please don't underestimate this step, a corrupted archive could result in lost funds.
These wallets connect to @remote-nodes and scan the @blockchain on your device, without sharing any key with the nodes. They provide higher privacy, but require more time synchronizing, since missing @blocks will be scanned only when the wallet is opened.
Monero has one of the largest communities of any open-source project. Monero researches, audits, and implements critical security and privacy technologies, which are user by millions worldwide.
To receive XMR you only need to provide the payer with an @address where they can send funds to. Most of the time it's easier to just share a QR code and let the payer scan it, instead of copy-pasting the alphanumeric string. With the GUI every generated address come with its QR code. Make the person scan the QR code with the Monero @wallet on their phone and receive your XMR in minutes. Remember you can generate as many addresses (subaddresses) as you want. This is useful if you want to keep funds separated for any reason.
Wait until the payment has arrived and has enough confirmations (The more confirmations, the safer the transaction is. You need at least 10 confirmations before you can spend the funds.).
When you create your wallet for the first time, an @address will be automatically shown to you. That's your primary address. If you want, you can simply use that address to receive payments. You should be concerned about who knows about this address (since one address in different locations can be associated), but you do not need to worry about blockchain observers watching transactions to this address like with Bitcoin. A friend can send transactions to the same address without reduced privacy.