You can always check out AGOL http://www.arcgis.com/features/plans/pricing.html
If you need to host on your own infrastructure, you can run ArcGIS for Server. A basic set-up for software only would run you 20k. This would give you a 4-core license - it's 5k for each additional core.
If you happen to package Esri with your product, like if you sell seats to a website which embeds ArcGIS Server maps and functionality, you may need an ASP license. A 4-core license for this would run about 40k.
Maintenance would run you about 10k/year (2500 per core). Keep in mind, you will also have expense in buying the server and for server maintenance. Additionally, you may need to spend some money on your network backbone.