First question if you are using LrC (Classic) you have a subscription to the Photography Plan which includes Photoshop, LrC, Lr (cloud-based) and Lr (mobile) apps and moving to the Lightroom (cloud-based) ecosystem which is Lr (cloud-based) app and Lr (mobile) apps and giving up Photoshop and LrC?
If you're going to export them as JPEG's and upload them to Lightroom for the cloud, why not just shoot JPEG images in the first place? JPEG images from modern digital cameras are pretty high quality. And if you are going to be working with JPEG images in Lightroom for the cloud anyway, why not just start with original JPEG's in the first place?
I've filled up my harddrive with RAW images in Lightroom Classic and have decided it's time to migrate to Lightroom CC.
What reasons do you have for migrating? Is it only a "storage" problem? Larger local hard-drives may be a better solution.
1. Will uploading hundreds of RAW images to the cloud take up a ton of storage?
Yes. 50GB on your hard-drives will need 50GB in Cloud storage. The (basic) Photography Plan only provides 20GB. For more you would need to pay extra. If you change to the Lightroom Plan you would get 1TB, but no access to Lightroom-Classic or Photoshop.
2. Is it better for me to export them as JPEGs, and then upload them to CC?
That is defeating a storage space problem by reducing the 'quality' of your images. (Throwing away the film 'negatives')
3. If I keep them in their original format, will their edit history also be available in CC? Just in case I want to access previous edits or revert to originals?
If you "Migrate" then yes. But limited. You do NOT have 'History' available in Lr. You only get the current edited state, a 'Step back of the last edit' , or total 'Reset'.
4. Once uploaded to CC, is it safe for me to delete them from LR Classic?
Adobe takes responsibility for Cloud storage, so Yes- Safe- putting your trust in Adobe.
My advice (with my bias towards Lightroom-Classic) is to-
1) Solve your storage problem with an upgade of local hard-drive storage. Either by larger internal drive/s or extra external drives.
2) Keep Lightroom-Classic as your prime 'Controller' of your photography database., with its better features and the modules (that are not available in Lightroom. eg. No Print module!).
3) If you want to use Lightroom (on mobile devices) -Sync photos from the Lightroom-Classic Catalog. (You do not need any of the 20GB storage for this.)