#1). Mauser pioneered the Mauser rimless rim at approx. .473 inches in the late 1800s. .308 Win/.7.62 NATO uses the same diameter but slightly greater thickness. Grab a catalogue with "shell holders" in it and look at the calibers for the same shell holder as 7x57 or .30/'06... This is your basic group of rounds.
#2). Mauser designed around a cartridge 57mm long. Uncle Sam, copying much, needed 63 mm to get the performance sought so Springfields were a trifle longer. US .30/'06 = 7.62mm x 63mm as I recall. Your standard 98 action may or may not work with the longer "'06" family of cartridges without being relieved. (.270 WCF mainly, although the .280 is in there. .35 Whelan too. Elmer Keith was much proud of a .33/'06; ".333 OKH".) So you pick and choose in the group based on length.
#3). As said, sometimes the shorter and less tapered .308 family works in the 98. Sometimes work is required to make them feed reliably. Many 98s were rebarrelled / rechambered for the 7.62 NATO following WW II. I think Israel did many. It can be done. .358 WCF is much ignored, but not puny... And there is a .33/.308 wildcat...
#4). If you want a scope, you will need mount holes drilled and the bolt "bent for scope." Not difficult for a machinist, but not free. I suspect your $200.00 for everything will leave you with a used Tasco for a scope.
#5). If you choose to open the bolt face, then you can have anything from the .6.5 Rem Mag up, just costs more. .350 Rem Mag was interesting but not much better than the .358 WCF. I think the standard "short magnums" are in the 68 mm long range. This design was around the Springfield rifles and a bit of a "stretch" for the 98. It would get you your .338 WCF Mag. You don't mention distance. Keep the range short and the .35 Remington has done the job many times. luck