Get the engine running so you can drive her around = this helps you by learning what your car is capable of, needs, etc (you may find you don't need a bigger engine). Purchase another engine to build a little at a time. Focus on the suspension for street/strip.
Brakes (rebuild them)- front disks, rear (disks or drum), manual or power brakes - alot of guys use manual on their drag cars (vacuum is low on high HP motors).
Rear End (gears/posi) - 10 bolt with a posi - purchase a good set of gears, not the ebay crap - get brand name here - it's worth it! Posi unit, use the factory from a camaro or s-10 4x4 or something, you can rebuild that to work for your strip use. Later you can build up a 9" rear end with a spool!
Tranny (rebuild performance shift kit) - if you have a TH350 now, get another and build it yourself for a street strip car. You can do this yourself and it's a great education for the rest of the car. If you want to get someone else to do it, call around but make sure they beef it up for the HP/Torque you want to run!
Interior (stock or modified) - since you're driving it, do the things that you need to do. Find some good gages and maybe a tach - radio is for old men and woosies:devil:
Listen to your engine breathe! That's music to my ears!
Set up a list of things needed to get it registered and on the road -
these are priority,
then set up a list of things you need to build to make your goal on the strip.
If you are shooting for 12's (great first goal!), then build for that - do lots of research online! (but don't believe anyone...ask for help and see what everyone else is running) There are plenty of guys on here that love to help noobs like yourself! In a few years - you will be teaching others!
Have fun!