Well Matt for once i have the ability to say BTDT got the bench to show for it.
I used that exact plan and you can follow the whole thread on my
construction of it here on our forum. I am still not completely done too many other projects keep getting in the way.
(Edit inserted after looking at the American Woodworker bench again.) Go for that one if i were you with the tools you have. Thats a real neat design. Just skip the tool tray, to me they nothing but junk collectors.
BTW mine started out as that bench then i got to read the Chris Schwarz book on bench design and that caused a few modifications like the addition of a leg vice to the side of the bench and the addition of a dead man (yet to be attached) .
I think for the cost its a great first bench. Its a user which in my mind is what a bench should be. All good and well making it out of the best lumber etc and having all the perfect elements but then when you finished although its work of art i could see myself not wanting to spill something on it or treating it like fine furniture.
I would say make sure you pick your lumber out. I learnt about what SPF stands for in the process and wish i had known before. Spruce Pine and Fir. Yup thats the mix at the HD. If you selective and can identify the differences you can try to pick out one of them. Today i would go for the the fir also feel the weight of the wood assuming its been reasonably dried.
I echo whats been said about your plane but if you have some real muscle and determination anything is possible.
Search on the forum for vice there has been much discussion on this topic and many have commented on low cost well made vices available. It does not always need to be top draw stuff.
Good luck and enjoy the journey.