I am new to trading. I want to trade BTC, LTC and ETH. If I don't want to keep the coin on the trading website, do I need 3 wallets for my coins?
Hierarchical Deterministic (HD) wallet technology is very powerful. HD wallets can be implemented as either software applications or dedicated embedded hardware devices that connect to computers or Android devices using USB interfaces. Trezor, Ledger, and Keepkey are three examples of hardware wallets that support the BIP 32, 39, and 44 standards.
BIP 32 is the foundation for HD wallet technology.
BIP 39 makes it easy to backup, restore or port all of your private keys typically represented by 12, 18, or 24 words supported in multiple languages. BIP 39 also supports hidden wallets with the application of as many extra passwords you so desire to provide plausible deniability services. The three hardware wallets mentioned above support passwords, albeit the Keepkey password support is still in beta testing. BIP 39 also prevents vendor wallet lock-in.
BIP 44 technology enables HD wallets to supports multiple cryptocurrencies within one software application or hardware device. Here is a complete listing of registered BIP 44 cryptos. Hardware wallets, tending to be the safest for holding large sums, support a subset of cryptocurrencies on this list. Software-based multi-currency wallets (e.g., Jaxx, Coinomi) tend to support more currencies. The last time I checked, these software-based wallets did not support BIP 39 passwords.
It is recommended to have your BIP 39 seed words loaded into multiple hardware wallets from different vendors. At times, backend servers associated with one H/W vendor might be down or transactions don't complete successfully, and the other manufacturer product will work fine. This is analogous to having multiple email addresses in case one server goes down.
If you are going to speculate then I am not sure how useful it would be for you to keep your coins off of an exchange (it might be possible that you won't be able to sell your coins because they are in transit to an exchange)
That being said, each coin (ETH, LTC and BTC) uses separate private keys to send the coins, you will need to have a wallet that stores each of these private keys (I also recommend that you do your own research on this before deciding on using any particular wallet).
Trezor is a hardware wallet that support multiple cryptocurrencies (including LTC/BTC/ETH if I am not mistaken) and you can use your trezor wallet to store all of the above mentioned coins.
EDIT: There has been a recent detection of a exploit on these device making them essentially exploitably by theft. Ref https://cointelegraph.com/news/trezor-releases-update-to-address-hardware-security-issue
I am sure there are many different wallet services that offer what you are looking for but trezor is one that seems highly recommended.