I wanted to make a wizard with a Transmutation focus, casting beast shape in most fights to get stuck-in with the fighters. I was curious how changing shape alters your character outside of gaining the medium/tiny size changes. Do you lose the ability to cast spells while an animal? Do your ability scores change to match the animal, or stay the same? Does your HP change? Those kinds of things.
Any other things to think about or reflect on when being the 'animal mage' would be helpful. As an aside, I wanted to be a wizard instead of a druid because many of the wizard spells are more appealing then being a druid, although druidic beast shapes are also appealing.
Polymorph effects have a section in the magic rules, most of your questions are answered by that.
You don't loose the ability to cast spells, but animals are incapable of performing semantic or verbal components.
You get bonuses and penalties to your ability scores, as given in the spell description.
You gain what the spells say you gain, plus ground speed, plus (for most of these spells) all the target's natural attacks includings proficiency with them (important: you have to recalculate attack bonus and damage bonus for these attacks).
You only gain abilities and modes of movement listed in the spell, and only if the monster possesses them. If the the monster and the spell have different values (which includes the maneuverability for flight), always use the lower one.
Example: You are a level 5 human Wizard with 12 strength and want to Beast Shape I into a Leopard. Human race features are independend from form, so you keep the extra feat and skill ranks. Your new strength is 12+2=14. You gain low-light vision, scent, and a climb speed of 20 feet (the spell would allow 30, but the leopard only has 20). Your ground speed stays 30. You gain a +2 natural armor bonus. You gain a bite with 1d6 base damage and 2 claws with 1d3 base damage.
Your BAB stays at +2, so your bite and claw attacks are done at +4 (2 from BAB, 2 from the new strength modifier). The bite deals 1d6+2 damage, the claws do 1d3+2 damage.
You do not gain a anything else - not the leopard's pounce or Weapon Finesse, not the fly speed mentioned in the spell.
You loose the ability to speak (but you can roar) and can't access your equipment, including the spell component pouch. Active spells like mage Armor stay active.
The problem with such a wzard is that you keep your BAB and HD, so you are very reliant on buffs for both offense and defense.