For faster and easier accessibility, you could always store all your ERC-20 tokens in a wallet line MyEtherWallet. If you have security concerns, you could always rely on storing different tokens on multiple addresses and keeping them backed up offline. Your token balances of new tokens from ICOs can be seen reflecting in MEW upon entering contract address, token symbol and decimal.
Thank you very much for your help.
You could store both your ETH and tokens all in the same single wallet address.
That's great.
1° Then will I see within my unique wallet my balance in ETH, Alt-coin1, Alt-coin2, ..., Alt-coinX?
2° If I want to transfer my Alt-coin2 to another address will it be possible to specify which crypto I want to transfer within those in my unique wallet?
Yes your altcoin balances will reflect on your wallet and yes you will be able to pick the specific altcoin that you will be sending.