Yes, yes yes! Without an amp, the speakers will not sound much better than if you re-ordered Toyota paper cone speakers. There is no substitute for a good amp, not even expensive speakers. If you'd like some ideas, I documented my audio install years ago including how I mounted the tweeters. Many say fitting the speakers are the hard part but I found the tweeters to be an ever tighter fit. The old Toyota tweeters are very tiny.
Thinking About Upgrading Your Sound System? Do It! - Toyota 4Runner Forum - Largest 4Runner Forum
Yes on the bracket. I ended up making my own out of MDF board but then again I did put 6 1/2" speakers in the rear for my passengers' delight. To fit a 6 1/2" in the rear though you have to trim the door panel and a slight amount of the storage pocket.
Yes yes yes! Your new speakers are literally screaming to be powered by an amp. No head unit has any decent amount of power it can put out. 15W RMS, 20W RMS, 22W RMS, all not nearly enough and you won't notice any difference then the stock head unit. I highly recommend small 4 channel amp that produces 50-75W RMS. Here are a few examples:
Sound Ordnance™ M75-4 Compact 4-channel car amplifier — 75 watts RMS x 4 at Crutchfield
Kenwood KAC-M3004 Compact 4-channel car amplifier — 50 watts RMS x 4 at Crutchfield
If you have your head unit already, look into seeing if they also sell an inline amplifier like I purchases for my Alpine.
It requires no wiring at all. That was the part I was dreading when I bought mine years ago so it was the perfect solution. Since then I've done other audio installs that required wiring and while it is a bit of work it's nothing impossible. The inline amplifiers tend to cost more but you save money by not needing an amp install kit and you save lots of time!
You really cannot go wrong with any amp that puts out over 50W RMS. The biggest restriction is size as that will dictate where it can be installed. Mine is actually sitting behind the center console tucked in behind the storage pocket.
One more edit: It is a rabbit hole. After you've bought a head unit for lets say, $250, an amp for $200, speakers for $300 more, brackets and wiring kits for another $100 you've now gone $850 deep. A small powered 10" sub or a compact powered 8" sub will run about $300 more. I really like the small 10" sub though as it adds so much depth to your music but it really does depend on what kind of music. I listen to mostly electronic and dubsteb so a sub is kinda a no-brainer. If you listen to mostly vocal, pop or instrumental types of music then a sub may not make a significant difference.