Image from the PC in the office to the TV in the living room?

I have a desktop PC in the office.

How can I transfer the image from the PC to the TV without cables? I have seen that there are wireless HDMI stations, but rather expensive and probably not so good.

If that is not easy to realize, an alternative would be:

I could use my laptop to access the PC in the office. What would be offered in the domestic WLAN? Remote Desktop of Windows or TeamViewer?

That's where MiraCast or the Google Chromecast variant comes in handy

A good alternative would be the Chromecast Stick.

The is connected via Wi-Fi and can reflect through various programs / apps the screen of the PC and the smartphone on the TV.

Various streaming providers, such as Netflix, also support the Chromecast.

This only requires an HDMI input on the TV. He is usually present on new TVs.

With the Chromecast, can I stream the entire screen of the PC, not just the Chrome browser?

It depends on what you want to transfer. A RemoteDesktop or TeamViewer session is great for typing in Word or reading on the Internet. However, fleet games with 3D graphics are unbearable. Photoshop suffers from the reduction of colors extremely. In addition, you probably need a back channel: With (wireless) HDMI, you can transfer the image, but to operate the computer, you also need mouse and keyboard.

It would be far cheaper and more efficient to buy a used laptop (200 euro) and connect locally to the monitor.

Right.