Printers are the work of the devil. Since time immemorial they have given trouble and even the best have been flummoxed by their antics. Invariably they refuse to work when installed, or break down when it is critical for them to do so. And the cost of ink and toner can make you weep.
With a bit of care choosing a printer does not need to be too painful. First of all you need to know what you are looking to do, and from there do a little research to ensure you buy a reasonable printer at a reasonable cost which will work with your computer.
There are essentially two different types of printer; inkjets and laser printers.
Inkjets are good low volume printers with fairly simple mechanisms. They work by squirting ink at paper and do a reasonable job. The key disadvantage of inkjet printers is the astronomic price of ink. You may well pay as much for replacement ink cartridges as for the printer itself. If you print frequently you will find them expensive to run. If you do not print often the ink will still evaporate. Consider recycling ink cartridges and perhaps trying refiller kits to keep ink costs down. Shop around for best prices.
If you like to print photographs you may need a more specialist inkjet known as a Snapshot printer. To get the best out of these you will need specialist paper and specialist ink. These are expensive. Consider using an online photo printing service to save your wallet.
Laser printers are more complicated and use a powder or toner to print. Toner does not evaporate. They are a little pricier and are best suited for more business oriented applications or for someone printing a lot. They are not so good for printing photos. The replacement toner and drum kits are expensive, but the price per page of printing is usually much less than an inkjet.
Colour laser printers need a variety of toners and so replacing a set of colour toners can be formidably expensive. A mono or black and white printer only has one toner to change. All lasers will need the drum changing eventually which will also be expensive. They usually last a few years.
Multifunction printers (either inkjet or laser) have additional capabilities such as scanning, copying and perhaps fax functions. They are known as convergent technology as increasingly they are preferred over a basic printer. The time comes when you need to scan something and then they become indispensable.
Before buying a printer do some research to ensure that you see as many reviews of whatever it is you are looking to buy. Check the price of renewing the ink or toner, that may be significant. Most printers these days need a particular type of USB cable, an A to B USB cable (or flat end to square end). Cables are cheap if you buy one online.
As regards printer compatibility with computers mostly things are simple. For Microsoft computers check that each printer is specifically compatible with your specific operating system. When installing the printer using the CD in the box try not to install spurious software which not uncommonly is included. For Apple computers check to see your system will work with that printer. Do some research if necessary. For linux do a search as it will most likely not mention linux on the printer specifications. Some printer manufacturers are diabolical, some have drivers if you look, others like HP support linux and out of the box, and an HP printer will normally just work.
When installing or troubleshooting a printer ask yourself:
Is it plugged in and switched on
Is the USB cable in place
If using wireless check settings at the computer and printer
Is the ink/toner in place correctly
Is the printer powered up
Has it been configured on your computer as default
Once set up and running a laser printer will last 3-6 years. Inkjets tend to last a lot less.