That is a very loaded question OP, and for a satisfactory answer you need to provide more details, but I will try to answer regardless:
- Are you targeting period-correctness or performance?
If you're targeting period correct hardware, then the Best builds you can have are Athlon 1200 + VIA KT133A chipset board or a Pentium 4 1500 + Intel i850 chipset board. These should be paired up with either a Geforce 256 DDR or a Radeon DDR.
The problem is, games of that era have.... dubious system requirements. For most games, minimum system requirements means what you need to launch the game - it doesn't mean it will be playable or enjoyable. Good examples of this are Dungeon Keeper 2 and Homeworld, both released in 1999. These games will however run well on the above configurations, but playability and enjoyability depend heavily on what resolutions, detail levels and the actual level of the game you are playing. 800x600 is generally OK for DK2, while 1024x768 32bit is ok for Homeworld, alltough there are situations ingame when framerates will sit under 30 FPS (last 4-5 DK2 levels, My pet dungeon, Gardens of Kadeshi level of Homeworld). The games you listed on the other hand should run perfectly smooth on these two setups, provided you do not exceed 1280x1024 resolution.
If you're looking for enjoyability, and as such performance, then you need to build a faster PC. Athlon XP 2600+ / Pentium 4 2800 Northwood are the minimum requirements for smooth gameplay across all levels in these 2 games. Pair these with either a Geforce 4 Ti 4200 or a Radeon 9500 and 1600x1200 32bit @ 60FPS is achievable. The games you listed will run great even on a Geforce 3 Ti / Radeon 8500 @ 1600x1200.
- Do you plan to use a CRT or an LCD monitor?
1998-2000 era 3d games look quite smart on an LCD monitor, provided you play at the panel's native resolution - 1280x1024 for 19" and 1600x1200 for 20 or 21" LCDs. On a CRT monitor even 640x480 looks quite good in my eyes, and for that resolution even your current build will suffice, provided you install a sufficiently fast video card (Geforce 256 SDR, Radeon SDR, Geforce 2 MX, Radeon 7000). I excluded 3dfx cards because in my experience a Voodoo 3 3000 was only able to provide an enjoyable experience in these games at 640x480 (particularly UT99 and Alice).
If you're using an LCD monitor, especially a 20-21" 1600x1200, then you'll want a Geforce 4 Ti4200 or a Radeon 9500/9700. Out of the two I prefer the ATi alternative for it's superior image quality, lack of driver "performance tricks" and excelent DVI support.
- What kind of money are you willing to spend?
If you want period correct and top end hardware, it will cost you. If you just want to be practical, then any Socket A or 478 DDR motherboard with a fast CPU, even socket 754/939 and LGA 775 (Intel 865/VIA KT800 only) boards with AGP are great budget options. Mostly any 754/939 CPU will work well for these games, same for most single core LGA775 CPUs.
As for video cards, the Radeon 9550/9600 are an excellent alternative to the aforementioned video cards. They are very cheap, quite fast and easy to source - the only downside to the 9600 and 9550 is the fact that most cards are AGP 8x (0.8V signaling) only, and will likely not work in some universal AGP motherboards (potential magic smoke danger) and will not physically fit in AGP 2x motherboards (keyed different), so keep this in mind.