My question is - do I need to do, well...anything in regards to the US? Does the US need to know I am getting married?
No, you don't need to do anything and I don't believe the US needs to know about your marriage.
However, I would definitely apply for UK citizenship before you move back to the US.
Your ILR only remains valid while you are living permanently in the UK. If you leave the UK for more than 2 years (i.e. move back to the US), you will lose your ILR and will have to start over from scratch again if you ever wish to move back to the UK. But if you have UK citizenship, you can come and go from the UK as much as you like for the rest of your life.
Will it become difficult if we do intend to move to the US?
No, it won't. In fact, it'll probably make things easier, because you will be able to sponsor a spousal visa for the US.
Does getting married in both countries do anything?
Not sure what you mean by this. You can only legally marry in one country, and then your marriage certificate will be considered legal in both countries.