I'm going to assume that your target is actually 1920x1080 and that 1920x1810 is just an error because I'm not aware of that resolution.
The moment you create a 1920x1080 composition it will automatically be a square pixel format and your source footage will convert to square pixel once you place it in the composition.
You don't need to do the intermediary step of creating a 960x720 composition. You can use "Detail Preserving Upscale" inside of the 1920x1080 composition and it will get you there in one step. I believe it's a 225% scale, but the effect will allow you to automatically scale to the height of the composition.
The end result should be a 1440x1080 image inside of the 1920x1080 composition with black bars on the side.
If you choose to the fill the whole frame you will either have to stretch the image horizontally making everyone look a little fat or scale the image up even further so that the top and bottom of the original image are cropped out but you will maintain the original aspect ratio. I personally don't like scaled up or stretched images, but it appears to be a common choice these days.
You do not have to change the frame rate of the footage unless your really, really want to. 60i and 60p are the same frame rate and realistically your footage originated as a 24fps source that has probably been through a telecine process to 29.97 fps.
All the frame rate variations can be very confusing and complicated but as long as your source footage doesn't have sync sound it's going to be hard to mess things up. However, if there's actually sound attached to the footage, changing frame rates has the potential to make things go south pretty fast. Without getting too technical an old rule of thumb is to keep decimal frame rates together (23.976, 29.97, 59.94) and whole number frame rates together (24p, 30i, 60i, 60p, etc.) It's difficult to explain working with different frame rates, which tends to require a lot of working experience (and some horrible out of sync deliveries) to really appreciate the issue.
There is possibly one other thing you will have to do. If your footage looks jagged or seems to have kind of a horizontal blinds effect running through everything, particularly fast movement, it's because you're originating from an "interlaced" source. In that case choose the source clip inside of after effects, go to interpret footage:main and select "separate fields". Most likely it will be Lower Field First, but if that doesn't look better then choose Upper Field First.
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