If I put down a Wild Card and choose a color, can I then also straight away play a card in that color?
No, you can only play one card per turn.
On your turn...
Example: If the card on the Discard pile is a red 7, the player must put down a red card OR any color 7. Alternatively, the player can put down a Wild Card...
Functions of Action Cards
Wild Card – When you play this card, you get to choose the color that continues play (any color including the color in play before the Wild card was laid down)...
Here's a great place to read the rules for yourself:
From mattel.com: UNO Rules 2018
No. After you play a card, the next player takes the next turn.
From the rules:
Wild – This card represents all four colors, and can be placed on any card. The player has to state which color it will represent for the next player.