It's nearly impossible to say what kind of hardware you need without considering all kinds of details. How often do your visitors access the site? How many pages do they click in a given time frame? Etc.
I am a developer for a site with approximately 100,000 registered users. Our LAMP box serves about 90,000 PHP page requests a day with no problems. A given page request might have anywhere between 5 and 20 database queries to a mysql database. The machine also handles email, DNS, spam filtering, and virus scans for a handful of email accounts (just our employees and forum notifications).
The machine's hardware:
CPU: AMD Athlon 64 X2 dual-core 2.2GHz
Memory: 1GB (i think it runs at 667 or 800MHz)
3 hard drives:
one for boot, /var, /tmp, /home
one for /backup
* one for mysql files
Peak traffic is pretty much happening as I write this. 'uptime' shows a pretty low cpu load:
[user@server ~]# uptime
13:09:54 up 146 days, 20:53, 1 user, load average: 0.40, 0.24, 0.20
Once you have a machine running your site, you can use apache bench to test it.