Patch Notes and PC System Specs

Man, it's not your gpu, i have bought a 1050 gtx to play it and it still has stuttering and drops in the framerate all the time. I play it on Medium, some stuff on low, but scaled to auto 1080p to get better visuals.
This grants me often more than 60 fps, but constantly it drops and keeps stuttering. I tried to put everything on low, the fps got even higher but the damn stuttering still there.
I have downloaded and ran some program to unpark cpu cores to get better performance but couldn't see any difference.
Don't know wtf happens with this game. It's not well optimized i think because i should be running it okay in high settings in 1680x1050 with no problems. I also use FXAA and SSAO because even if i disable them, he suttering continue

Patch 1.05 information added to OP.

Rising the power limit won't damage anything, the card will overclock itself whenever it can (although slightly). You can then fiddle with actual overclocking by rising the clock of both memory and core (this is an example, notice how the priority arrow is pointed to power instead of temperature). The worst you can get is a driver crash, only way to damage the card would be to rise the voltage too much but you don't even have to touch it on your card.

Optimize what you have as much as possible. Maybe buy a better cooler for your CPU (there are good, inexpensive ones like the CoolerMaster Hyper 212 EVO at around 30$), as that would help keep that chip more stable under full load.

If you want to fiddle again with settings I recommend turning off Ambient Occlusion as the first thing. SSAO isn't too heavy (you still lose a few fps), but HBAO can cripple low and mid range cards. Shaders, effects and meshes also are better on low with your hardware, while you can probably get away with textures on medium or high.

Another good trick is to put the Windows power profile (in control panel) to high performance instead of balanced. This will help keeping things more stable under stress, as balanced can decide to throttle back things when a lot of power is in use.

In the nVidia control panel go to the Manage 3D settings, then Program Settings, select ME:A (or add it if it's not on the list) and set the power management mode to prefer maximum performance.

One thing that's easy to check for is the utilities that may be available for your card based on brand. For example, I use EVGA's Precision utility to safely overclock my card. 

My PC:
I5 4690K, 16 GB RAM, GTX 970 4GB with a bit of overclock, SSD 250GB, game installed on SSD.
Monitor FullHD.
I play with everything at maximum/ultra except shadows on Medium.
The game is pretty good, pretty stable, I am not measuring FPS in game but I don't see bad FPS or FPS drops.

Very happy with the Frostbite engine

THIS!

Added option to skip autopilot sequences in the galaxy map

Did you just patched in separate setting for motion blur that is the best thing to happen to this game since launch 10/10 would not blur again. Now i can have post processing and no blur hecking revolution.

Well, looks like I'm staring at a total system replacement; the video card slot on my PC just failed out of the blue. Still has power, but cards aren't detected. I didn't even know that was a thing.

Money's gonna be tight around here until maybe the fall. I'm considering picking something up on the used market until I have the cash for a proper build. So, what's the cheapest machine that people are getting tolerable performance on? Figure 1600x900, medium textures and mostly low FX stuff.

There was a thread about this. The fix is to go into "Documents\BioWare\Mass Effect Andromeda" and take your saves and put them on the desktop. Then just delete everything else (except Screen shots if you have them, they can go on desktop as well) and run the game again. It should run just fine after that. Check to make sure Origin made a copy of your saves or put the saves from your desktop and Screen shots back into the folder. That should fix it for you. It worked for me, at least.

A prompt should appear on the bottom of the screen. Simply press the key/button displayed.

Note: the skip prompt will not appear if banter is currently playing.