Win98 doesn't natively support WiFi in any form, so you're completely dependent on the drivers of your card/adapter for WPA supplicant. No surprise given that Win98SE was from 1999, and WPA was defined in 802.11.i-2004, so is five years newer.
CPU usage is dependent on both NIC design (does it offload?) and on encryption chosen - TKIP or CCMP(AES). TKIP is computationally lighter, but is almost never accelerated in hardware. AES is harder, but there's more hardware offload. Even Via C3 CPUs (very much Win98-era) had a unit for that. WPA allows both standards, WPA2 is essentially the same as WPA, but mandates the availabilty of CCMP-AES, where it was optional in WPA. It's worth playing around with these settings if you encounter problems. Note that WPA1/TKIP is theoretically insecure, but - unlike WEP, which in some ways is worse than no encryption at all - in practice it's no major risk unless you're doing something sensitive, in which case you shouldn't be messing around with old crap on that network anyway.
The biggest disadvantage to allowing TKIP is that 802.11-2012 mandates that all High Throughput performance enhancements (i.e. the stuff that makes WiFi-n faster than WiFi-a/g) should be disabled if a station connects using TKIP. That not only nerfs your old stuff, but potentially newer devices associating on the same network might select TKIP instead of AES and be impacted too. For optimal performance you should run WPA2-only/CCMP(AES)-only - but when you're talking about getting Win98 online, you might need to compromise for the sake of compatibility. If your AP supports multiple SSIDs with separate security settings, you could potentially get the best of both worlds by broadcasting separate WPA2/AES and WPA1/TKIP SSIDs. Only issue here is that you increase overhead with multiple SSIDs, although each SSID is 'only' about 3% of airtime in 2.4GHz - but with multiple APs that adds up fast.
