In our hands, a good-enough PromethION run generates about 80 Gigabase of sequencing data, corresponding to ~25x coverage of a human genome. The raw data of such an experiment is about 1.4 Terabytes of fast5 files. If you don't really care about nucleotide modifications or improved basecalling you can just delete those fast5 files and work with the fastq data (about 80 Gigabyte). The corresponding BAM (using minimap2) is about 100 Gigabyte, and it's worth converting to CRAM to get these smaller.

I can't conclusively answer the VCF file question, as you should probably tell me which variants you are going to call (structural variants, small variants, both), and it will depend on your variant caller. Regardless, the VCF will be really small in comparison with the rest. SVs called with Sniffles are about 6 Megabytes, SNVs called with Longshot are about 220 Megabytes.