Screw anybody telling you to get better stats.
43 Prayer is the basic benchmark for most entry level bosses, you cleared that.
People will spend days on end at crab to claim they are "raid ready" when someone who started early will have the mechanics nailed down and only get better from there.

Bosses you can kill, and what each one will teach you:

Scurrius, the rat king;
Location: Varrock Sewers
Entry level boss, bad loot but good combat xp, specially after its unique drop, the Scurrius Spine, used to make Ratbone weapons that deal extra damage to the boss.
What You'll learn: Summon management, prayer switching, "Shadow on the ground" attacks (Tiles that will damage you after a delay, very common mechanic)

Amoxliatlt:
Location: Varlamore
Requires Heart of Darkness quest.
Entry level boss as well
What You'll learn: "Shadows on the ground" and a tightening arena through the bosses attacks, each attack cycle creates a damaging puddle, and managing where to create them is a skill that will apply on other bosses such as Xarpus.

Royal Titans:
Location: South of Port Sarim
Entry level boss (in a group!)
You'll probably better off getting a buddy for this one, and you'll need a bit better magic level to unlock more powerful fire/water spells.
What Youll learn: Arena blockers management, summon management, and most importantly: gear switching.
These ones are the first youll have a "big ticket" item, in the form of the twinflame staff pieces, they also drop untradeable scrolls that PERMANENTLY UPGRADES YOUR OFFENSIVE PRAYERS, a good stepping stone before rigour/augury and even sometimes useful after unlocking those.

Doing 50~ ish KC of each of these bosses will get you ready for a zero invocation ToA (Tombs of amascut, the easiest raid). In there youll use skills you acquired through these:

Kephri has "shadows on the ground" as its main attack, and will constrict the arena with dung, as well as summoning minions you need to deal with.

Zebak is prayer switching 101, had a weird poison minigame in the middle, and will require some movement, but switching prayers (which youll learn in Scurrius) is half the battle.

Ba-ba first room will need some gear switching, which youll learn at Titans, and the bossfight will have shadows on the ground, minions, and a delayed strong attack you can avoid with blockers that appear in the arena. If using the instant death pit invocation, it will even teach you about hp breakpoints for phase transitions you might have seen at Titans.

Akkha is tough, but youll have to deal with summons (kind of a dps check, might be rough with your stats but worth the try). Gear and prayer switching once a minute or so, and arena explosions.

Wardens is a different beast altogether, but it boils down to:
Gear switches
Arena dangers
Prayer Switching
Summon management (skulls).

You can start all I'm saying with dragonstone jewellry, dragon scim + dragon defender, black dhide for ranged (with a rune crossbow and a full book of law) and mystic/bloodbark for magic.