All the martial classes are kind of lame in core-only, but rangers and paladins especially so.
They don't offer much in core-only and benefit massively from expanded book access, both through feats and ACF's.
While barbarians also benefit from more books they're probably the best off.
Monks are always trash even with all the books. In core-only they're a buff commoner with some party tricks.

A lot of this also depends on your combat style. Archery, TWF and sword & board suck in core because of the lack of available bonus damage.
You basically need to be a rogue (for sneak attack) to make archery or TWF viable.
Basically if you want to be a viable mundane character in core-only you'll be a str-based THF melee with Power Attack or a rogue. Since neither paladin nor ranger offer anything to support that you'll probably be best off as a barbarian with an optional fighter dip.

If i played in a campaign like that at all i'd probably go for a sorcerer, depending on how annoying those inconveniences are. Damage spells suck anyway, go for summoning or BFC.
You can make a viable sorc with divination + conjuration and wouldn't have the spells known for massive versatility anyway.

A cleric would work too but i'd be too annoyed at the nerfs (specifically the limited spell list) to enjoy it.