It might be worth mentioning that with regards to the Chips in the OP it's probably a more reasonable selection if you actually intend to use the built-in AMD Graphics; if you don't, and plan to use a separate dedicated graphics card, than other CPU which trade the Radeon graphics for other features probably make more sense anyway. Because of that I'd say that when building a system using it one can probably only "worry" about Memory in terms of the current inflated prices.
Right!
However, They say 'Best budget CPU' now is an Intel Pentium G4560. With the money you save you can get a good graphics card. 
Not a horrible plan. It would, of course, depend specifically on one aims to be doing with their system, and I think there are other considerations.
PROS:
Great Price, as you said- Right now, the G4560 looks to go for 77.99 CAD on Amazon.ca (I'm too lazy to switch to amazon.com for USD price comparisons here...)
There are upgrade options to more capable chips on that same platform/socket.
More money of the initial cost can be put towards a better graphics card.
CONS:
It uses the LGA 1151, which is a number of years old. This can be a "limiter" preventing the use of some of the more recent CPUs (including the ones you note in the OP, of course). I built my current system in 2014 and it is using a i7 4770K which is one of the more capable CPUs available with the socket.
feasible upgrade options may require motherboard support/consideration up-front to avoid a motherboard replacement, which may mean the system needs a more expensive motherboard.
As above, it will also be a "limit" factor in terms of things like Memory, which means you are "stuck" with DDR3.
IMO, The cons are hardly a factor unless you are chasing benchmark scores, or playing the latest games on amd settings and even the smallest framerate dip makes the game "literally unplayable". And I expect, over time, the price of the "upgrade" from that Pentium CPU to something more powerful will drop considerably. On the other hand, you can get lower-end CPU options for later platforms/sockets for similarly reduced prices, which may very well be a better all-around option depending on the specific goals.
