What is the real speed of my internet connection (cables, routers, and internet subscription)?

[greatcan448]

I'm really confused about this "internet connection speed" thing. When I buy cables, there are gigabit cables, etc...when I see routers, it says 54 mbps, 150mbps, etc...and when we signed up for an internet connection, it says that our internet speed is 1mpbs...so which is which and how does one affect the others (I'm talking about cables, routers, and internet subscription here) when it comes to my internet connection? Thank you very much in advance!
This is a follow up question...Does it mean that it doesn't matter which cable/router I will buy (besides compatibility) because I only have 1 mbps connection?

[Mackey]

Data will flow through your network at the speed of the slowest link. If your Internet connection is throttled to 1 Mb/s, then the maximum rate you will receive data from a remote Internet site is 1 Mb/s.