That's a good manual to have. I like the Haynes manuals too, they are more explicit for newbies and spell things out better IMO.
What worries you about the spring compressor? It is essentially a set of hooks connected by a threaded rod. Put the hooks on either end of the spring and use a ratchet to bring the sets of hooks together, thus compressing the spring.
You need a comprehensive set of sockets, preferably in 3/8 and 1/2 inch. 1/4 inch is good to have for other projects, but not as much needed on suspension. Sockets should be 6-point, especially for suspension work where you're cranking down a lot.
You will definitely want a couple breaker bars, one shorter and one longer. If you need an extra set of sockets to fill in the gaps or for some deeper sockets, consider getting a no-name brand of hardened impact sockets. These should be plenty strong even if they are Chinese crap.
Check the torque values for the major bolts you'll be installing. If they're all in the same range and fairly high, you may not have much of a need for a torque wrench if you're tight on budget. I prefer to use one, but as long as you don't severely under tighten or severely over tighten something, it will be fine. If you've got the cash, get one though. Again I got a Craftsman on clearance, but I'd just say avoid the Harbor Freight ones.
A jack and jack stands, both with enough height for you to get under the car and work comfortably.
Discount places to shop include Northern Tool and Harbor Freight. I personally use Craftsman sockets & ratchets because I've had good luck with them and found some big sets on clearance or sale. My other tools are definitely a big mix. I wouldn't recommend Harbor Freight stuff for important pieces like ratchets or the spring compressors - all their stuff is cheap Chinese crap.
And pick up a can of penetrating oil to help loosen rusted bolts. I'm blanking on the brand name - I can see the bottle in my head: white can with lots of writing all over it, yellow cap. Someone fill in the blank for me
When you take the strut off the car, look how at how it is assembled and use it as a guide to assemble your new parts. Pay close attention to how the spring seats on the strut mount.