67 plymouth barracuda fastback 273/727

You can upgrade your rear suspension with H.D., X H.D., or even S.S. springs. Add an 8-3/4" sure-grip rear end, with some type of gear (3.23, 3.73, 3.91, etc., etc.), and you'll have a pretty stout set-up.
Front suspension should be o.k. You could add a front sway bar, change over to the large bolt pattern, and disk brakes.
You can use any LA small block for a swap, 318, 340, or a 360. All have more torque and H.P. than the original 273's did, and they like to run wide open as well! The 273, 318 and 340 even share the same stroke (3.31"), and rod length (6.123"). Alot of the components will swap between those three engines (fuel pump, P/S, A/C, etc.), without any modifications.
Your trans is fine. Maybe freshen it up when you are ready to do your engine swap. Maybe even a new torque converter to go with the cam your going to get and install!!
Watch for ads for used components (BBP disk brake setup, springs, engines, rear ends, etc.), to do your build with. This will keep the costs down. Some things you will want/need, to buy brand new.
You are doing the right thing by asking questions here. That is what this site is all about. I'm sure other members will chime in with their opinions as well. Take all of them into consideration on your build.
I am currently building a 340 to take the place of the 273, then the rest of the drive train will be updated/upgraded, when the money will allow for it. The 904 will be rebuilt, new torqure converter, and an 8-3/4" sure grip with 3.91 gears as well.