It has been a while since I played but I don't recall many negative consequences to staying in hollow/undead form in Dark Souls 1 (unlike demons souls where it reduced your max health).
While hollow you can't be invaded by other players but you also can't summon other players or npcs to help with difficult areas or bosses and you can't kindle bonfires while hollowed either.
Kindling a bonfire raises your maximum estus flasks restored by that specific bonfire by 5 each time to a maximum of 20 iirc. I wouldn't kindle every one but it can be handy for difficult areas or bonfires that you use a lot in central locations. You can always briefly go into human form to kindle and then kill yourself to go hollow again if you want to avoid invasions.
In certain areas there are also npc red phantoms that spawn when you are in human form that usually have unique or better than average loot.
I would probably stay in hollow form most of the time at the beginning until you get used to the game. It can be really frustrating when someone with a griefing build invades you at low level and immediately breaks all of your equipment leaving you with a big repair bill.
TL,DR: You can stay hollowed most of the time to avoid invasions but there are some situations where it is beneficial to use humanity to become human (summoning, kindling, etc). And if you want the full Dark Souls experience you need to fight off a few invaders at inopportune moments.
