I have read about a lot of problems regarding nvidia graphics cards and Linux. I would like to know:

Which Linux distribution would be best for my system? Or does it not matter? I would primarily use Linux for programming.

If anyone could give other advice to go about this that would help avoid unexpected problems, that would be great. Thanks.

Perform a google search for nvidia compatibility and the distro you want to use.

I don't have a Lenovo but I do have three computers running Ubuntu Linux and they all have nvidia cards. Two of them use the same video adapter and, while they are supposed to be compatible with Ubuntu and the proprietary nvidia drivers, they are not completely compatible. I also have a Dell laptop with an unknown nvidia video adapter model. It works beautifully with the proprietary drivers. All three machines work with the nouveau drivers, which is good enough for developing business type applications.

Ubuntu is moving to the Mir compositor soon and other distros are moving to the Wayland compositor. The rules regarding compatible video adapters could completely change in the next year.

I have a Lenovo SL400 that took a flawless install of Linux Mint. Installed everything in one pass.

I also have a Dell M4500 that has Nvidia video card and I put Linux Mint* on it and the video card is a 1gb dedicated which shows up correctly if Windows 7 is installed but in Linux it only shows like 256meg. So I found actual Nvidia drivers for nix and they installed no problem.

01:00.0 VGA compatible controller: NVIDIA Corporation GT216GLM [Quadro FX 880M] (rev a2) (prog-if 00 [VGA controller])
Subsystem: Dell Device 040c
Flags: bus master, fast devsel, latency 0, IRQ 16
Memory at e2000000 (32-bit, non-prefetchable) [size=16M]
Memory at d0000000 (64-bit, prefetchable) [size=256M]
Memory at e0000000 (64-bit, prefetchable) [size=32M]
I/O ports at 7000 [size=128]
Expansion ROM at e3000000 [disabled] [size=512K]
Capabilities: <access denied>
Kernel driver in use: nouveau

I have a stack of Dell M4300 laptops (all Nvidia) and I installed Ubuntu, Mint, Slackware, RHE, Kali, Fedora. I have not experienced any issues installing Linux on any of them. I am not qualified to give linux advice but from my experience you just install whatever linux that you like the look and feel of and just go with it.