If i order an iphone can i connect it with my company?

So I found an iPhone 5s on Amazon and I want to order it but I don't know if I can connect it with my company, T-Mobile. Will I be able to do that? Or?

Impossible for us to know without knowing the carrier of said iPhone (Verizon, Sprint, AT&T, etc)

If it says it's "unlocked" without a carrier name, the answer is probably yes, it will most likely work

If it says it's "AT&T unlocked" it will work

If it says it's "GSM unlocked" it will work

If it says it's "GSM" it will probably work

Basically there are two types of phones, phones that work on "GSM" and phones that work on "CDMA". It's magic cell phone stuff, best not to ask how it works. T-Mobile and AT&T work on GSM. Sprint, Verizon, and US Cellular work on CDMA. In general they are not usually cross compatible however in some cases they can do both (I believe sometimes you can use CDMA on AT&T).

As for the "unlocked" part, basically, carriers are obnoxious and try to "lock" phones to their network to make it harder to switch to other networks. It is now illegal to withhold the "unlock code", so in theory you can buy a phone that is NOT "unlocked" and on AT&T, call them, and have them "unlock" it, however I don't think it'll be worth the hassle.

If you are buying used make sure it has a "clean IMEI" and no iCloud lock

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