A question to certainly start your computing adventures.
Firstly and foremost your budget has much to do with your final decision. Lets take a few moments to look at the other elements that will influence our buying decision.
Desktop or Laptop/Portable?
Fundamentally your first decision should be do I want to be mobile and travel with my computer. This does not mean you need to travel outside your house. It may just mean you want to move it from where you normally use it, in your office, to show your pictures to family over coffee or watching a programme on BBC iPlayer whilst in the kitchen. If you do want portability then a laptop would be your best choice, otherwise you may be best off with a desktop.
There are differences other than portability though. In general you will get better specifications on a desktop than on a laptop. The main reason for this is the need in a laptop for all the parts to be as small as possible and use as little power as possible. Many laptops now do not come with a builtin DVD/CD drive, so if you want to use DVDs or listen to CDs then you will need to take this into account.
A laptop also comes with a screen whereas in general a desktop doesn’t. Most laptops have a 15 inch screen but some are smaller (11 to 13 inches), some are bigger (17 inches). Generally the bigger the screen the heavier the laptop. With a desktop you can purchase virtually any size screen you wish to. If you have sight problems the desktop route may suit you better as everything will view at a larger size.
Memory and Hard drive?
Generally speaking you should buy the most memory and largest hard drive you can afford.
The more photos you tend to have the larger the hard drive you should have. A normal user taking a few photos every week, using the internet and email would be fine with a 500Gb (Gigabyte) drive. Alternatively, a keen photographer with many photos and video would be best going for 2Tb plus (Terabytes) which is 2000Gb.
The same basic rule is also true for the amount of memory you should have. Many computers come with about 8Gb of memory. As a basic rule though, you can never have too much memory. Depending on your choice of computer you can often add more or change the memory at a future date. Be aware that computers such as the MacBook Air can not have more RAM added after you have purchased it.
Software and Applications?
When you buy a computer it sometimes comes as a surprise, but software such as Microsoft Office are an additional cost.
In general you will have a web browser, email program, image viewer, media player, basic text program and perhaps a basic video editor with the computer you buy. You will also get promotional or trial applications installed, for example antivirus software and perhaps Microsoft Office. These are only trial versions which may last a month or so and then require you to purchase it in full. Ask the retailer what is included.
On some computers you will get more software. For instance an iMac includes a word processor (Pages), spreadsheet editor (Numbers) and presentation creator (Keynote). This is a nice touch Apple have included, as this covers most of which a basic user would require without any additional costs. Bear in mind though that an Apple device is normally more expensive, but not always.
Applications can also be added at any point after getting your computer. Start with the basics supplied and build from there. There is usually a selection of applications that do the same basic function but at varying costs.
My only rule of thumb though is to obtain software from a trusted source, NOT just anywhere on the internet.