first of all I'd go AMD because it is cheaper and performs very well.
Motherboard: I would suggest an nforce2 mobo. Either the Abit NF7 (S) or the Soltek 75FRN2 (L, R or RL). The former has more features than the latter, thus is more expensive. It also has the SoundStorm onboard sound which is said to be a lot better than any onboard sound and even better than some of the most popular sound cards (like the Audigy for example).
CPU: An Athlon XP 2500+ will suffice. It's highly overclockable and despite the fact that it's locked, the multiplier is right where it should be at 11 so you have headroom for overclocking. (comes with an hsf but if you wanna' overclock you WILL have to buy a better one. I suggest one from Thermalright. Note that the Soltek board doesn't have mounting holes so if you choose that board, you will need a heatsink with clips)
RAM: Don't skimp on the RAM. Get at least 512mb of PC3200 and I suggest Kingston (I am very pleased with their value ram). Corsair is said to be better but is more expensive. Big B (a mod here) likes Samsung a lot also.
Video Card: That's a tricky part because the new cards will be out very soon so you can either wait for those or buy now. Right now the best of the best is the 9800XT from ATI. It's also quite expensive so if you can get your hands on a 9700 Pro or 9800 non-pro or pro you'd be set for a long time. However if it's still too expensive, you can go for the 9600XT or Pro which is a mid-range card that can play all the recent games out there. The current line of nvidia cards have problems in DX9 and image quality so you'll have to wait for the next generation of cards if you really wanna' go nvidia. Also, don't listen to those who say that ATI drivers suck. They're not that bad really. I use the catalyst 3.10 and they work very good for me.
Hard Drive: I only buy Western Digital. They have been reliable to me and I suggest you get one of those. Get at least a 80gb one because the price/value ratio drops a lot if you go below that. I'd say that right now the sweet spot is at 120gb.
Optical drives: LiteOn is very popular. I've never owned one but it's supposed to be a great manufacturer. I have a Samsung and it's still running after 3 years so either one of those companies is good. Of course, Plextor is the best, but is more expensive.
If you're on a budget and would like a DVD drive, you can buy a DVD/CD-RW combo drive.
PSU: Never try to save money here. Get a good and reliable one from Antec. I suggest their TruePower series and either get the 380W or the 430W. I'll get back on this topic shortly.
Sound card: you can skip this one for now if you're on a budget as every board now has their onboard chip. It's not comparable as external sound cards but it's not that bad either. You'll be able to live with it.
Case: Get a big one because it's easier to work with, you have more space for drives and allows better airflow. I personnally suggest the 1080AMG or 1000AMG from Antec.
the 1080AMG comes with 3 fans, with space for 2 more and comes with a Antec TruePower 430W. So if you buy this one, you're set for the psu. the other one is the same exact one except that it comes with no psu, no fans but a side window. It's cheaper of course. The fans that come with the former are standard fans which push a good amount of air but they're a bit loud. They are decent though.
Mouse and Keyboard: I love my Logitech MX500 (mouse). It has a nice design, it'S big enough for my hands (I have big hands) and has good ergonomy. As for the keyboard, I use a basic Compaq keyboard and it suits me fine. However, Logitech has an MX duo which is wireless (the mouse is the MX700, it'S the same as the MX500 but wireless) I personnally wouldn't go wireless because I don't want to have the responsibility of recharging the mouse. But a lot of people love the combo.
Speakers: I bought the Logitech Z-560 which is a 4.1 system and I like them very much for games. You'll have to tweak the sound a little to get what you like though. It's ok for music but was apparently not made for that imo. If you wanna' go cheaper, there are the Z640 from Logitech which cost half the price and are 5.1. Big B also did a review on the Creative Inspire 4400 :
http://www.zone365.com/content/17/7/1
I highly suggest you listen to the speakers before buying them because sound is a subjective thing.
Monitor: I have a LG and I hate it, so I can't see myself recommending this brand. Of course, you can't go wrong with sony but you pay much more than what you get because of the name. You'll have to go and watch monitors because image is also subjective. Reliable brands are NEC and Samsung. I have an Old 14'' Nec. It has to be 20 years old and it still works. I'd personnally go for one of those two brands.
And finally, one of the most important part of online gaming is your internet connection. You will definitely have to go broadband here whether it's DSL or cable. Cable is faster though so I would suggest that as it is not more expensive (at least it isn't where I live)
You may notice that what I'm suggesting is very similar to the system described in my sig, it only means that I practice what I preach ;)
P.S. If you want a good FPS , you have to look at Rainbow Six 3 : Raven Shield. The Single Player is good but hard. But the Multiplayer is really what makes that game shines. I just can't get enough of it. It's not just a shoot and kill FPS, it's a tactical FPS so you have to think before you act and you can't rush because you have a very good chance of dying. Another great one is Medal of Honor.
EDIT: This is by no means a barebone system, especially with the case I suggested. I have the 1000AMG and it's extremely heavy when everything's inside. It weighs 35 pounds alone so you can only imagine what happens when you fill it with peripherals and components: it gets very heavy. However, I think it's the best option for you as what you're looking for is a gaming pc.