Below is the output of "df -h -a" command on my Nook Color running CyanogenMod 7.0 ROM (2.3.3) which gives you a break-down of the mounted partitions:
Filesystem Size Used Available Use% Mounted on
tmpfs 244.2M 44.0K 244.2M 0% /dev
devpts 0 0 0 0% /dev/pts
proc 0 0 0 0% /proc
sysfs 0 0 0 0% /sys
tmpfs 244.2M 0 244.2M 0% /mnt/asec
tmpfs 244.2M 0 244.2M 0% /mnt/obb
/dev/block/mmcblk0p2 69.5M 107.0K 69.4M 0% /rom
/dev/block/mmcblk0p5 440.5M 142.8M 275.0M 34% /system
/dev/block/mmcblk0p6 941.9M 347.7M 594.2M 37% /data
/dev/block/mmcblk0p7 341.8M 39.3M 284.9M 12% /cache
/sys/kernel/debug 0 0 0 0% /sys/kernel/debug
/dev/block/vold/179:17 7.5G 5.7G 1.8G 76% /mnt/sdcard
/dev/block/vold/179:17 7.5G 5.7G 1.8G 76% /mnt/secure/asec
tmpfs 0 0 0 0% /mnt/sdcard/.android_secure
/dev/block/vold/179:8 5.0G 57.0M 4.9G 1% /mnt/emmc
Out of 8 Gigabytes of internal memory ~500 MB is reserved for the ROM itself (/rom and /system), ~1.5 GB is for app storage (/data and /cache), 5 GB is for data storage (/mnt/emmc) and another ~500MB reserved for other miscellaneous Android operations. You can also see my 8GB SD Card mounted on /mnt/sdcard.
Keep in mind that these partitions can be (and usually are) remapped based on the needs of a given ROM.
In terms of your question regarding apps from the Market, there are some limitations that mostly depend on the type and version of the ROM you are planning to run. The biggest concern the screen resolution and LCD density. Several apps, including the Market itself (Vending.apk) are quite picky about how well (or even if) they will work properly. Most common side-effect is apps displaying in a tiny window instead of properly scaling. Most can be fixed by disabling Compatibility Mode in Spare Parts, but some (e.g. Google Reader) will only function with a certain LCD density that could be in conflict with other apps.
Keep in mind that most of the custom ROMs for Nook Color are works in progress, so expect to see better compatibility with all apps going forward. Also, if rumors of Froyo (2.2) update for the official Nook Color firmware are true, we could see better performance once the official display/video/audio/etc. driver upgrades are rolled into custom ROMs.