You are most likely going to want to lease a VPS to run a full node, and whenever you spend funds stored in your wallet, your private keys are going to be temporarily unencrypted in your VPS's RAM and you would be exposed to possible side channel attacks. If you were to lease a dedicated server then your monthly bill would be very expensive.
If this is the case... might be a good pull request. Last time I walked through the OpenSSL code, they were using secure buffers... encrypted memory. Yes, it would stand to reason that the key for the membuffer would be somewhere in there as well, but that turns the hack into more of a needle / haystack problem rather than a simple memcat.
If I dont do it on the web, then what is the standard process of running bitcoin core as a hot wallet?
I think some on this thread are juggling terms. I (possibly in err) define a "hot wallet" as a wallet that is running on a machine that has a network connection. I define "cold wallet" as a wallet running on a machine that has no network hardware. So yes... 99.99% of the wallets out there are "hot" since you usually need a soldering iron the make a machine "cold". By that terminology, "hot" does not imply "hot+server". Most people run on "hot" machines and simply don't allow incoming peer / RPC connections. Most run apps like electrum. They simply keep their wallet on their phone. For the security guru's... they pull out the soldering iron and make their machine "cold". Then they spend their coin on their cold machine and carry the transaction over to a hot machine to transmit. Term is "sneaker-net".
Those are costly solution. So, is it the case, that blockchain.info or similar APIs are the only solution to send/receive bitcoin in a secure way ?
Good Lord no!!! Keeping your private keys yourself is generally considered safer than using a web-wallet. Some web-wallets have high praise, and may be good options for you, but there are certainly those here (me) that believe being in position of your own keys, although hard, is the most responsible thing.
Easiest thing... just grab your favorite Android / IOS wallet and figure out how to back up the wallet regularly. Use this app to send / receive coin. 80% safe (possibly more)