Sometimes cheap is expensive.
I apologize for being critical but I feel like this is helpful for a lot of people wanting to save as much money as possible. 
Okay, in the short run it might save you money. What do you sacrifice? How does it affect the long-term upgrade path? Pay less and you get less. Avoid paying slightly less money for much less product! It gets to a point where the feature and performance downgrade is massive but the price difference is minimal.
One example: you save 15% on smallest SSD. But you lose 50% capacity. Price per GB is almost twice as high. Really worth it?
Because of how an SSD works wear will be significantly increased when it’s low on space. Be sure that the cheapest SSDs will be tiny and have QLC (one cell split into 4 voltage ranges. As it wears it’ll be harder for the controller to distinguish between 4 levels. When it reaches a certain wear level you’ll see corruption and read errors (basically it’s dead or the usable capacity has shrinked even more)). There are also quirks where write performance suffers on low space (because the smallest area SSDs can write to is a block. When low on space you are forced to re-write a bunch of data to fit the new data in. You only save a 200 MB file but in reality the SSD is writing much more (thus wearing it down a lot faster).
The internal controller will balance the load between different cells. Also, read performance benefit from fragmentation unlike a harddrive. So it’s opposite to an SSD in many ways. Very exiting topic but it’s off-topic.
Isolating the price makes it an arbitrary value.
So, here’s my proposed strategy for “cheapest laptop” (I insist on bending the established rules):
Re-use old hardware?: Do you have parts in an old laptop that can be re-used?
Buying used parts: When you’re already compromising the total product you might as well buy used. That way you at least aren’t spending so much money and the sacrifices cost less.
CPU: cheapest one, you sacrifice performance and bang for your buck.
RAM: One stick with reasonable frequency and timings (find a sweet spot, avoid wasting away performance by crippling the CPU. A ridiculously low frequency will be detrimental for performance and is not worth a few bucks saved). A decent stick provide an upgrade path (long-term planning). You avoid having to buy two sticks when you upgrade because the first you bought was… well… garbage.
You may lose 5% performance or you may lose 50%. Is it worth saving 20 bucks? Find the sweet spot. I’d guess 2666 to 2933 MHz to be quite cheap. I did a quick search and 3200 MHz cost basically the same as 2666 MHz. Don’t go too low. 2133 MHz is too low (not worth it). 1600 MHz is a major facepalm. 
Timings matter, they’ll be worse. In memory scaling articles they tend to align timings. So the real world difference might as well be worse.
SSD: You get what you pay for. You’d have to get a QLC drive with low performance. Look at GB per dollar. Look for reviews so that you at least choose the best cheapo SSD. The trick is to avoid the absolute cheapest SSDs but go slightly more expensive to gain a larger capacity, longer NAND lifespan and performance. Don’t forget to consider BfyB and the value you are actually getting.
Wi-Fi: Get a budget model from Intel. This accounts for such a small percentage of the total cost anyway. The cards from Framework are so cheap it’s pointless saving a few bucks.
Charger: Here you can actually save some bucks (along with the disadvantage of possibly increasing carbon footprint). Buy a cheap 65 W charger on Amazon, Aliexpress, Taobao, Banggood etc. Preferably with multiple outputs so you can charge both phone and PC.
Modules: you can torture and cripple yourself by just buying one module (the USB-C one). This is down to preference and how much you want to suffer to save money. 
OS: Obviously Linux. There’s no best distro, they all have their strengths and weaknesses. Some generally better than others, though, some more optimized for laptops.
Bottom line: This might not be what the premise of the thread asked for but I think this is a minefield of pitfalls and a lot of people aren’t aware of what it cost to save just a tiny amount of money. The price you potentially pay is a dramatic reduction of performance, a nightmare that comes from limited storage space, significantly reduced component lifespan and just in general pretty bad bang for your buck. Most of the lowest priced products aren’t there because they are meant as genuinely good alternatives. Many of them are pointless.
It wouldn’t physically fit, the slots are different. The general rule of computer hardware is that “if it doesn’t fit, then it’s incompatible”.