Training is a big part of runescape, and without it, even traveling through white wolf mountain can get you killed.  So what to train on, and better yet, how.

First off the why, as you know, it looks cool, you can kill bigger badder monsters, and get bigger prizes.  And of course, wouldn't be complete without killing that one monster that took your most valued item, and slaughtering him, her, or rather it over and over.

There are four basic character types when fighting is concerned

Regular melee-Training attack, defense, and strength and just smashing things.  The main cost is food, as they will be able to easily hit you back.
First, get some money and buy bronze, iron, and steel full armour and weapon of your choice.  This is not needed, but is extremly recomended, it's easier to fight monsters with the best armour and weapons you can wield.  Why buy all three?  Those first levels fly by fast, and don't you want the absolute best weapons and amours?  So what to train on-  Fast and simple, train on something weak and that there are a lot of.    Chickens, cows, goblins, all near lumbridge for the lower levels, then barbarians at barbarian village,  dwarfs near ice mountaian and on,  When you reach about level 30, Pirates on brimhaven, near the agility dungeon.  Next off to giants at around level 40.  And if your a member, do the start of the elemental shield quest and kill elementals for a while.  This will be one of the best monsters for a good while, but you can also kill baby blue dragons.   Then you can kill trolls, ice warriors or ice giants, or whatever else you find easy to kill and slaughter.    For higher levels, I suggest lessers, dragons, greaters, or something to that effect.
The second option is always fighting something harder, you would however need a lot of food and a lot of bank runs, which is a hastle.

Prayer-These battle melee, but use prayer.  This mainly means using level 43 prayer and a lot of prayer potions.  It's not too expensive, and gets to be less expensive as your prayer level goes up.  Same monsters as for melee fighter, but you will need prayer points as well.  This means bone collecting, the best place to do this is the wilderness.  Pretty much north of between edge ville and Varrock  You can also buy bones, regular giant and dragon, if you are rich that is.  Also, if your melee is high enough, you can kill giants or ogers.  With prayer, you can easily kill higher level monsters.  You can also use potions with prayers, super defense super attack super strength and all the prayers you want/need. 

Ranger-These guys hit fast and don't get too beat up on the way, you save on food, but have to either fletch arrows if a member, or buy them all.  If you are killing high enough level monsters, that may cover the cost for your arrows.
What to train on-First off, always find a way to kill without them being able to kill you.  This is very important.  It is also wise to  first buy leather armour, and increase your defense level, just in case.  And of course buy arrows or fletch if your a member.  I highly recomend not buying anything above steel for training.    So what to train on.  Cows, chickens, goblins are good to start with.  You can just stand behind the fence.  You can kill jail gaurds by the jail in dranor village, and kill wolves on white wolf mountain, with this one stand on one part of the mountain, and shoot wolfs on another.  You can do the same thing with the ice giants and ice warriors also on the mountain. 
You can also kill the level 100 trolls by standing on one side of the rock and hoping they stay where they spawn, you can do the same thing with giants.  Also, one of the better ones, in the taverly dungeon, kill lessers through the gate.  For higher levels, there are a lot of great places in the wilderness.

Mage-Again, fast and hard and you save on food, but higher levels get to be pointless, and less new spells.  The runes used cost more then arrows and food combined.  This is the fighter type for the rich.  Buy full zammy robes, don't over pay too much, you'll need the money.  Buy runes, or craft them, but you can't craft death, and chaos can be troublesome, as the place to turn the essence to runes is in the wilderness.  But once you have all your runes and full zammy, follow the same monster guide as put for the ranger.  Same basic principle, hit them without yourself being hit.

And that about does it for training, happy runescaping.