Yes you are able to switch to using segwit enabled wallet and send your bitcoin to it, but it will cost you some fees, because of big centrelized wallet services like Coinbase and Blockchain who have not yet supported it, switching from them to a segwit wallet will come at a cost, your transactions may have lower transaction time and lower fees, but you are going have to buy a harware wallet like LegerNano S or Trezor who supports this technology.
Switching to Segwit will save you money in long term, especially if you send coins daily.
Blockchain itself hasn't supported Segwit yet(You can't search Segwit address on Blockchain), but it's just a minor problem as there are Segwit block explorer already.
Transaction time are still the same as your transactions will need to be included to a block, just like non-Segwit transactions.
Segwit are currently supported by Electrum, don't buy yourself a hardware wallet if your goal is simply just to taste Segwit.
Im thinking if i need to change my wallet to a btc wallet with a segwit.
Whats the difference between btc wallet and btc wallet with segwit? Is it possible to transfer btc from my btc wallet to btc segwit wallet? Is it better to use the wallet with segwit?
Just create and send your coins to a Segwit address as usual, it's good for the Mempool and your TX Fee