Getting Familiar With Debian's Releases
Prior to making any major change to your computer you should ALWAYS backup all of your work. While the Debian Installer has been extensively tested, it cannot prevent you from making mistakes nor a prevent a power failure in your city while you are installing your new operating system.
Refer to Debian Releases for more information about the Debian versions, but the following ideas may guide your decision.
Choose Debian "Stable" if you want the computer to just work for a prolonged period of time, without the risk of new packages breaking your habits or workflow. In most cases, when people talk about Debian, they are referring to Debian "Stable". The network install images for stable (buster) can be found at http://www.debian.org/CD/netinst/
If it is important to you to have recent packages of all the installed software continuously rolling onto through Debian, and you are fine with constantly downloading and installing updates that may stir up a bug every once in a while, you may choose Debian "Testing". The network install images for testing (bullseye) can be found at http://www.debian.org/devel/debian-installer/.
If it is important to you to have the absolute latest packages available in Debian, you should learn about Debian "Unstable". There are currently no network install images for unstable. If you want to install unstable, download the image for testing and upgrade to unstable by editing /etc/apt/sources.list. However, unless you want to test the installer for testing, the better choice is to use the stable installer to install a minimal stable system and upgrade to testing and then unstable as described above.
Choosing The Appropriate Installation Media
There are two main choices of installation media to meet your needs.
The network install image
For those with broadband Internet access it is often preferable to use a minimal network install image, rather than download a full set of 650 MB ISO images. This network install ISO (called "netinst") contains just enough packages to install a basic Debian system. During the install procedure only the required packages are downloaded from the Internet, making it more efficient overall. A netinst iso image is around 180 MB.
If your wireless network card is not recognized by the installer you might consider doing the installation using a wired (ethernet cable) connection or installing using a different network card. In any case it may be preferable to install with a wired connection for bandwidth reasons or simply to defer wireless setup until after the initial installation.
If you have no way of establishing a network connection during the installation, then you will need to install using full installation CDs or DVDs.
The full "CD/DVD" image
These images are for those who need all available packages that are in the current "stable" release of Debian.
Although there are over 30 CDs (or 5 DVDs) in a full set, only the first CD or DVD is required to install Debian. The additional images are optional and include extra packages, that can be downloaded individually during the installation, or later.
An updated installer that supports the newest hardware
DebianLive - Debian Live CD / DVD / USB
InstallFAQ - Including how to install unstable (sid).
FAI, Fully Automatic Installation
PackageManagement - Managing your system
Debian GNU/Linux Installation Guide (all architectures, stable branch)
PXEBootInstall - The manual for setting up a netboot server.