Apart from the Animated Shield, is there a way to fight with a shield (given that my character has proficiency with shields), and attacking at distance (I also have proficiency with some ranged weapons). Since ranged weapons are two-handed, it's seems very difficult to have a great defense and a ranged attack (that I'm aware of, I'm still pretty new to this game).

My goal is to still have the +2 AC while attacking ranged. I want to do it in a cheap way (Animated Shield is too rare and expensive). I have too little HP, and I want to stay far from combat. I already have studded leather armor.

I already had the idea of crafting a shield/bow (Is it possible to build a custom weapon, and if so, how will my character be able to use it?), but it seems very impractical at best.

If it can help, my character is a Rogue (Scout)/Ranger.

Use thrown finesse weapons and the Sharpshooter feat

Thrown weapons only require one hand to draw and throw. You can use your free object interaction each round to draw a new one each round. This just requires you to be carrying enough to get through a combat encounter or two.

As a rogue, most of your damage will be coming from Sneak Attack, so the smaller damage die of the weapon won't matter so much. You do need to use a finesse thrown weapon, however, to activate Sneak Attack. The best option for this is the dagger or dart. The dagger has the added benefit of being useful in melee, but the dart is cheaper and lighter, which makes it easier to pick up a bunch of them.

The dart and dagger both have range of 20/60, so if you are throwing them beyond 20 feet, you will have disadvantage and lose the ability to use Sneak Attack. The solution to this is the Sharpshooter feat, which allows you so throw up to the weapon's maximum range without disadvantage.

Alternative: Grab the Dual Wielder feat

The Dual Wielder feat will give you a +1 to AC while you are dual wielding, and allow you to draw 2 weapons per turn. Have a dagger in each hand and you can attack twice per turn (once with a bonus action) for only the loss of 1 AC compared to using a shield. It does cost a feat, but this can be a good option.

The quick answer; spells.

Rangers, and Arcane Tricker rogues, both eventually get spells. So you can hide behind a shield with one hand free to cast spells. But I don't think that's the answer you want.

More in line answer; thrown weapons.

There are a number of one-handed weapons that have the "thrown" property. They are weapons that you can hold in one hand, but you can throw them a short distance. The problem is that they are still considered melee weapons and will use the character's Strength bonus instead of their Dexterity (which I'm sure you're hoping for). It's been pointed out that the dagger and dart also has the finesse attribute so it qualifies as using your Dexterity bonus.

However this will allow you to hide in the back, use a shield, and still get some distance between you and the bad guys while screaming "Not in the face!"

Double checking your post, you want 30 feet. Of that list, almost all of them max out at 20 feet before going into the disadvantage spectrum. However, the javelin does make it the full 30 feet.

From the comments, I see you are not yet proficient with shields so in the meantime.

The Cloak Of Protection is an uncommon magic item that raises your AC and Saving Throws by +1, though it requires attunement.

Glamoured Studded Leather is a very nice upgrade to your studded leather, though it is Rare. The Glamoured armor raises AC +1 and it allows you to change the appearance of the armor as a bonus action, non attunement.

With one Rare and one Uncommon item you would have the equivalent of a shield, while keeping your hands free.