The biggest decision that you need to make when buying a domain to use as the address for your web site is to decide on the name you are going to buy. There are a couple of aspects to this. First is which top level domain you are going to choose to have your domain within and secondly the domain name itself.
The top level domains that are two characters in length are country specific - each belongs to a specific country. In some instances the country administer their top level domain themselves and restrict its use to businesses and individuals within that country while others make their country specific top level domain available for anyone to use. Countries such as Tuvala (.tv), Federation of Micronesia (.fm), Montenegro (.me) having decided that they don't need an entire top level domain for specific use within their country allow anyone to use their domain. One thing to remember though is that although they allow anyone to use it now the domain still belongs to the specific country and so they can change their mind at any time and restrict access to people resident in their country.
There are also a few three character top level domains that were created way back at the start of the internet which are also country specific and which in fact are specific to certain types of institution within the USA. These include .gov, .edu and .mil which were allocated for the specific groups originally using the internet before it was opened up so that everyone could use it.
The other three to six character top level domain names are intended to be used for international web sites. In some instances such as with the two six character top level domains .travel and .museum the use is restricted to particular types of web site (some countries also apply this type of restriction with the second level domain names used within their country) and so you would only be able to get a domain within one of those top (or second) level domains if you meet the qualifying requirements. Other top level domains such as .com, .net, .org, and .biz are available for anyone to use for any purpose whatsoever (with these four the popularity of use is basically the order I have listed them and so you would usually prefer to get the one closest to the start of that list which hasn't already been claimed).
So depending on where you are and the purpose you intend for the site there will be a number of top level domains available that you can use and also a number that you can't. The first decision that you will need to make is to decide which of the ones that you can use that you would like to use.
Of course you can't use a domain name that someone else already has and so if you have decided that you want a specific name on the front of your domain name then your choice may be further limited by others having already claimed that name within some of the top level domains that you could use were that name already claimed. If this occurs then you have a choice - you can either pick a different top level domain where that name is not already claimed or you can choose a different name that is still available for your chosen top level domain. Which of these you choose will depend on how badly you want that specific name and what use is already being made of that name with existing sites which may or may not clash with your intended use.
Where a domain name has already been claimed then it will either point to an actual web site where it is being used or it may just be parked (where it basically points to a placeholder page with the person having acquired the name either for future use or in the hope of selling it at a later date to someone prepared to pay a significant amount for it). If the domain is used for an actual site that deals with the same topic as your proposed site then you will probably be better off if you select a different name for your domain so as to not compete with that existing site (with their probably having the advantage due to having been longer established and probably also having the more popular top level domain). If you are covering a completely different topic then using the same name on a less popular top level domain will not be such a problem as the two sites will be easily distinguishable by the topic they cover (although even in this situation you might consider a different name so as to avoid the issue of some of the people looking for your site ending up in the wrong place). Where the already claimed domain name is parked then setting up with the same name on a different top level domain is even less of an issue as if a site ever does get set up on that domain you still have the advantage of your site having existed first.
Having selected the domain that you intend to purchase the next decision is how long to pay for at a time. Domain names are never actually owned by the individuals and companies using them - only the top level domains are actually owned by the country or domain authority that they have been allocated to. The actual domain names are only leased for a given period of time. With some top level domains you don't get a choice on how long you pay for (for example all of the .au domains must be purchased for two years at a time). With others you can select shorter or longer periods (usually .com and .net etc domains can be purchased for anywhere between one and ten years at a time).
The final decision is who to buy your domain from. There will be a number of authorised domain registrars who the domain authority has authorised to sell domains within a particular top or second level domain. There may also be a number of resellers who those domain registrars allow to sell on their behalf. In some instances the resellers may be offering domains at a cheaper price than the registrars they are reselling for as the discount the registrar gives them for buying domains from them in bulk is large enough that the reseller doesn't need to add back on the entire discount when deciding on their selling price.
If you are buying a domain to point to a web site then none of the other features that the various domain registrars and resellers offer as a part of their package will be relevant - everything else you need will be provided with the web hosting that you purchase - and so there is no reason for not going with the cheapest price on offer that allows you to use your chosen method of payment.