Just like the resolution has an aspect ratio... your menu needs to maintain an aspect ratio. So create your menu on whatever resolution and define the aspect ratio. You need to use basic algebra to solve for x type math to determine how your menu changes.
If your menu maintains the same aspect ratio then it will not get distorted. Define the aspect ratio for ALL rectangles and make sure they maintain when res changes. Sounds like a couple moving parts so maybe not straightforward but doesnt sound impossible to do.
Remember aspect ratio is the width of something over the height. So determine an aspect ratio for your menu rectangles u are happy with and maintain them on all resolutions using algebra. Id have to do it myself to figure it out but maybe i will and write a small forms app to show it.
Positioning menu doesnt really need to consider aspect ratio as much as the size of the rectangles unless u need rectangles to maintain a distance between each other that scales. So Im only talking size. Example if u just want your menu 10% down from the top of screen and 10% into the right of the screen your X and Y on all aspect ratios will be 10% of res width and height respectively.
And if your menu has multiple rectangles then u need to position one rectangle relative to resolution and all other rectangles are positioned relative to that rectangle.
edit... i made this so far... i use a windows form to represent the game and a panel (blue) to represent a rectangle u would draw in game. I am able to maintain aspect ratio when i change the "game" (form) resolution but it is not perfect and buggy. I use decimal types for calculations but i think it goes off a little when i am casting to ints. Anyways i am doing this for my first time and i almost feel like it would be easier to create the menu with different settings predetermined for each game aspect ratio than to calculate dynamically. I do like challenges though so ill try to figure it out...