Storing money is good decision and i will recommend Bitcoin wallets. All said that wallets will be risky and hacked, it is foolish. Bitcoin is developed under decentralised secure system.

Never trust any exchange. You don't know who you are dealing with. Numerous exchanges have fallen with their owners running with the money. This is why im also reticent to give them my real data. I dont know who is getting my data and what are they going to do with it. Given the precedents I just try to use fake names and VPN to not give them any data about me because bitcoin exchanges aren't properly regulated so it can be a mistake to give them your details along with the risk of losing your BTC.

Just buy the coins then put them in your wallet.

Well, I keep bitcoin in online wallet because I know that my bitcoin and money is safe and secure. In addition to that, putting in online wallet will help you to keep your bitcoin safe.However, some people and bitcoin users keep their bitcoin in offline wallet or hardware wallet that you need to install to your computer.

I do prefer bitcoin wallet because with BTC wallet,there is security. It offers bookkeeping, portability and simple ways to give and receive cash.It’s rather like an online bank account, but even simpler to use. Each BTC is a unique solution to a mathematical problem, consisting of a short string of text which represents a figure. Let’s say you give someone a coin or fractional coin – the text string changes as it enters their wallet, and once a global network validates the transaction, your original coin is invalidated and the new coin becomes theirsoffer security. It offers bookkeeping, portability and simple ways to give and receive.

I also prefer bitcoin wallet since it's safe and very versatile it can also your way of investment  but I don't kept it on one wallet i made different account, i also buy gold and keep it as an additional investment

bitcoin is very safe to store money now a days. its very fast to receive our money back when we want which no other money exchanges can't do now a days. it can be like a investment for our money with safe hands of bitcoin.

Usually, people usually say the safest place to keep money is bank. Previously when bitcoin is unknown, I also think so. I do not deny the bank's safety. But when you keep the money in your wallet is much safer, bad guys are hard to steal my information.

I think the best way to save money is to put it in a very secure wallet like coins.ph or blockchain becuse if you only store your money in exchager like waves, bittrex or others it may able to go down the value and sometimes because of advnce computer it can be hacked and then it will all gone in just one snap.

Pros of saving them at an exchange would that you'll be able to buy/invest any altcoin instantly, providing they are also present in that exchange. That is probably the only pro for this.
But cons are many, security, losing all your funds, not actually owning your money, not able to buy instantly, or send funds to someone instantly.
Recommendation would be to always save on your own wallet, and only keep that amount on funds you would like to use for trading.