Which one you like better? The calibers I am most considering are .243, .260 Rem and 7mm-08. I mainly just want a lightweight, compact rifle to take with me in the vehicle, use around the home or to even take with me when I go out hiking here on my rural property. I'll likely opt for a stainless model with a synthetic stock and some sort of quality scope in the 2-7 power range.

For general use purposes, which caliber would you prefer? I'll likely end up handloading two equal weight bullets, like the Nosler Partition and Nosler Ballistic Tip, to give me deeper penetration or fragmentation, depending on what I want. I'll do my best to get them both shooting to the same POI. It may get used on nearly anything, ranging from coyote to deer and everything in between.

Right now I am leaning toward the Remington Model 7 SS in .260 Rem, with 100 gr Nosler Partitions and Ballistic Tips as preferred bullets of choice, loaded by me with IMR 4064 to a velocity around 3000 fps.

In my opinion, the Rem. 700 is typically quite a bit more accurate and has a better trigger "out of the box". I recently sold a Ruger 77 International and replaced it with a Rem. 700 Classic, so right at this moment I may be a bit biased--the Ruger wouldn't group for shit (pretty sure a bedding issue with the Mannlicher style stock), with ANY factory loads I tried which was many. The new Rem. loved my handloads (already loaded for another rifle) from the first try. Didn't even try factory loads.
My other 700, a BDL, Has the best trigger I have ever felt on a new out of the box rifle, and is a grouper also.
But, my wife loves her stainless 77 M.II, even with its six or so pound trigger (and she can hit with it--she told me "don't mess with it or get rid of it")  

ETA: I believe the .243 is a very under-rated rd. and is a true handloaders cartridge
MY 2 CENTS

I also recommend the Model 7.  I have three of them, two in 7mm-08 and one in .243 Winchester.  They are all excellent shooting guns, and the triggers are very easy to adjust (if need be).  The best thing about the stainless Model 7 is the barrel is 20" long, whereas a blued version has an 18.5" barrel.  

The .260 would be an excellent choice in the 20" barrel Model 7, but I would personally lean more towards 120gr bullets.

I too would go with the Model 7. I am I am not even a Remington fan.
My uncle has two Ruger M77 .308 compacts. He shot two deer with it last year. The Ruger shoots nice groups and is very light weight.But it feels like a kids' gun. If you are over 6 feet it will feel like a toy.  

I do like the fit and feel of the Model Seven over the Ruger. It fits me well, and feels like a nice light rifle, instead of a youth model.

I would get it in .308 but a .243 would be a nice handy rifle too.

And a 2-7 scope is a nice choice too.