Is Wales considered its own country, part of Great Britian or part of the United Kingdom?

Yes, yes and yes.

Wales is a country (by the broad definition of country). It is on the island of Great Britain, so yes, it's part of Great Britain. Wales is a subnational unit within the sovereign state of The United Kingdom of Great Britain and Northern Ireland, so yes, it is part of the United Kingdom.

Don't get hung up on the word "country" because that word can be used in many different ways. It doesn't even require a definite border. Example: "We just entered mountain lion country" - an area where mountain lions are found. Wales is viewed as a country by the Welsh people, so it's a country. But it is a different type of country than France or Brazil. Wales is not a sovereign state because the central government of the UK remains supreme. The United Kingdom is an example of a unitary state. Scotland, Wales, and Northern Ireland have a degree of autonomous devolved power. But such devolved power is delegated by the Parliament of the United Kingdom which may enact laws unilaterally altering or abolishing devolution.

Wales is a country but a sovereign state under United Kingdom or Great Britain. Shares same currency, official language, immigration with the rest of UK and is under the rulership of the Queen. There is a Wales football team same way as is an English team, and not a Great Britain footy team. Meaning that it is recognized by most organizations (eg FIFA) as a country that it is

Wales was once considered its own country before 1282, and had its own distinctive cultural group. Currently though, Wales has long been a part of the United Kingdom.

Wales is a country. It is part of Great Britain and therefore also part of the United Kingdom of Great Britain and Northern Ireland.

Before 1282 you needed a 'passport' to enter Wales. You don't now. It is still it's own country with its own language, Welsh. It is part of the UK so it's kinda whatever you want it to be. I just call it a nation. There are 3 original languages in the UK (English, Welsh and Gaelic) yet Polish is the second most widely spoken language in the UK, after English. - Just a little added extra ;)

Yes, own language and sports teams which compete in all major tournaments under the Welsh flag.

Part of UK