Connecting the EV3 to the PC may be achieved most easily with an ethernet connection - for that you need to purchase a USB to ethernet adaptor (dongle). The ethernet connection should 'just work'. However, most EV3 users do not own such adaptors and in that case the easiest connection is via a USB cable.
Connecting the EV3 to your PC directly with a USB cable is another easy and reliable way to make a connection. Connecting with a USB cable is described in the Install EV3dev page and video.
Having to use a cable can be quite cumbersome in many circumstances, however, especially when developing mobile robots, so a wireless connection is often preferable.
Bluetooth support is built into the EV3 brick whereas the use of WiFi requires a WiFi dongle to be purchased and attached to the brick. WiFi has some advantages in terms of range and reliability, and some disadvantages in terms of increased power consumption and the need to buy the WiFi dongle. Also, using WiFi requires that the EV3 be connected by WiFi to the same router that the PC is connected to, which may not always be possible.
By the way, it is possible to have more than one connection from the brick to the PC (e.g. by USB and WiFi simultaneously) but this is confusing and therefore not recommended. In any case you can only be 'online' (connected to the internet) through one connection. Note that when Brickman says you are 'Connected' it means the brick has a connection to the PC but is NOT connected to the internet via this connection, and 'Online' means that you are connected to the PC AND to the internet. Another simple way to test whether you have a working connection to the internet is to type ping "www.google.com" (or any other site) at the command prompt to see if you get an error.