Hey,
So when you send money from blockchain to circle, I should get a new circle (receiver) address for every transaction right
No, circle is an account not a wallet. There is no reason to request a new deposit address.
However, do you also need to change my blockchain (sender) address?
Thats not possible.
Or do I just send from the same address every time, or do they automatically change it for me? Not sure how this works.
Technically there is no "from" address. Blockchain explorers and wallets show it that way to make it easier for us. Whenever you create a transaction it used previously received inputs. Essentially old transactions. These old transactions have been received on a certain address. This address is put into the "from" part whenever there is need for one. To be technically correct it should show the transaction itself. Anyway. That is the reason why you can never change the "from" address. Its always the one you have received the coins with. If you have a wallet (not using a service like circle). It makes sense to hand out a new address every time to expect a transaction.
Why? Mainly for two reasons.
#1 It makes it harder for someone to know how much bitcoin you have. If you give out a fresh address every time, the address will show no previously received coins. Thus the person does not know how much you received in the past. Due to the way most service work it does not apply there. Mainly because while you have a deposit address, the coins received there are used for other users payout. Thus it might be possible to know how much coins you ever deposited to a service, but not how many coins you currently have. This is also only possible if you let people know your deposit address, which should not be a regular thing.
#2 It makes it easier to track from whom you have received coins. If you label your addresses accordingly (e.g. "full node donations - 1...", "load to user xyz - 1...", etc.) you never have to guess why someone send you coins or where they got your address from. Think of an address not like your bank account number, but like an invoice id. It helps you keeping track.
I just don't want to perform any action that will make someone more easily be able to hack me.
None of this has anything to do with security[1], if anything it is about privacy.
[1] Besides some possible highly unlikely future scenarios where bitcoin itself is in danger due to several algorithms beeing broken.