What kind of pump should I use to make compost tea?

I would like to make aerated compost tea this year.  Last year I would put some worm castings, and some compost into a bucket, stir it around for a few minutes and apply to the veggie garden.  This year I would like to try making compost tea in a 5 gallon bucket and aerate it.  I have read lots of stuff on permies, and watched many videos on the internet.  It is one of those things that you get to much info.  Everyone thinks there way is the best.  It's confusing and frustrating!
I have a small to medium size veggie garden, and several flower beds, and a rose garden.  I grow organically.  I just started chop and drop this year.  I have been adding compost (organic compost I bought at the store)  every time I have a new planting season, which is twice a year.  I also add other stuff depending what I have at the time.  Like Worm castings, azomite, rock dust, bone meal, blood meal, organic fertilizer, Organic chicken manure. You get the idea. Mostly it's compost with a handful of this and or that. All of my veggie beds are raised. 3 are normal raised beds and 3 are hugel beets.  I'm doing what I can to build healthy soil to grow healthy veggies.  In the raised beds I probably don't "need" to use compost tea, but I would like to give it a try.  Seems like it might give the veggies a boost, and help with soil health.  Also I'm planting veggies in an area that was just a weed patch last year.  It has had wood chips on it for 6,8 months, I don't know it was late summer early fall, I don't remember lets say less then a year.  Those veggies will probably need some extra help.  I also put veggies on a hugelkultur that was finished in August of 2019.  
I don't have a lot of money, so cost needs to be reasonably low.  I have a 5 gallon bucket, I don't want to bigger at this time.  I don't know what kind of air pump I need.  On another forum a person was very specific about the pump needed, and I thought yes finally!  When I looked it up the description fit both an air pump and a submersible pump made by the same company.  Fish air pump, pond and or hydroponic pump, submersible pump, a pump that makes the water pour into the bucked creating splashing.  there are probably more.  Do I need to buy one of those bags, can I use an old shirt, or just dump the stuff into the bucket?
The gist is I don't want to spend more then 35.00$,  I don't want to have to buy 500 parts that I can't find anyway, and I don't have degree in engineering to put it together.  If anyone would like to help put me out of my misery, I would be very grateful.  Thanks

I believe all you need is something that will bubble air into the water.  So I'd look for either one of those fishing bait buckets with an aerator or go to a place that sells aquariums and get one for a fish tank.  One of those should be under your $35 amount.

Here's one that could do two buckets at the same time for $18.  At least I think it would work...

aquarium air pump

Think about an aquarium.
Pretty much any air pump will work for a 5gallon bucket.
But a 1000gph pump for 5-15gallon and 1800gph pump for bigger setup

The real problem is the "air stone/bubbler". It gets clogged with the slimy bacteria film.

Container ... 5gal or 55gallon
Worm Compost Bag --- (Any cloth/mesh sach)
Air Pump ...... 1000gph or 1800gph+ (pretty much any pump work)
Air Tube .... (any type work)
Bubbler/AirStone .... (some folks have a long flexible "pool noodle" type air stone, other folks just punch a multitude of holes in a tube)

I've had great success with these guys;
https://www.ecoplususa.com/shop/bybrand/eco-plus#category=water-aeration
I personally like the "commercial" models but I'm hard on tools and they are bullet proof. I think the cheapest commercial ones are about 40$ but it would be ready to go.
If you can keep it dry the other models should do the trick and start at like $10. I would recommend getting one of the bigger ones for like $20 and instead of an air stone just get one of the metal air manifolds and stick that into the water to avoid the scum buildup that S Bengi mentioned

I was driving myself crazy trying to decide which air pump to get.  You would think it was a matter of life and death or something.  I ended up getting the small 18$ one.  I decided since I don't have a job at the moment, and I'm new to making  compost tea I should start small.  If I decide to make larger batches in the future, I can upgrade the pump then.  
I got the pump today.  Tomorrow I will make a bag for the compost/worm casting, I have a bunch of muslin, so I thought that would work and not cost me anything, and be super quick and easy to make.  I think, hope that will work.  I will put my worm castings and compost in the bag and start a batch.  Bubble for 48 hours and I'm good to go.  I have heard use it 50/50 tea to water, and I have heard use the tea 10% and 90% water.  For veggies what do you all do?  Thanks for your help.  Looking forward to giving my veggies a treat.

I'll have to try this at some point; presently I just pee in a bucket and dilute with 10 parts water. If you want more potatoes just snip off a branch and put it in damp sand in a shady place. I did that and two weeks later when I transplanted it back to the bed it had tiny potatoes on it.

Sad but true I already regret my decision.  My thought was I don't know what I'm doing, start small.  I'm suppose to dilute the tea by at least 50%. That means I will have 10 gallons of tea, that should be plenty.  The reality is it isn't nearly enough.  I have 6 raised beds in my veggie garden the sizes very, but the two smallest are 4'X4' The largest is about 3/X6',  and two in-between. If this is all I have I would be good.  But I also have a 20'? Hugelkultur, Then I have planted several fruit and veggie plants in, I don't know what to call it, I don't think it qualifies as a food forest, but It was an unused space between the back of our garage, and two apricot trees.  I filled the space with wood chips months ago.  I guess I will call it my wood chip garden.  Then there are fruit trees, a rose garden and several small flower beds.  I don't know why I was thinking a 5 gallon bucket would be what I needed.  I guess I will just have to constantly have a batch brewing.  I've read I'm suppose to use the tea on my veggies twice a month.  Maybe if I time it right and plan it out I can make enough so everything gets tea a couple times a month.  Oh well live and learn.

Could you just get a 55 gallon blue plastic drum and upsize your operation?  Maybe the same pump would handle a bigger tank?

Jen, don't fret! I personally don't agree with diluting compost tea. Instead I prefer to spread around the undiluted tea, even if just a splash here and there, onto soil that has already been watered with plain water (or is otherwise already hydrated and ready to support biological allies).
My logic is that dilution disrupts the equilibrium that the biology has settled into in the brewer and could cause blooms/die offs of certain species. In fact, the farm I work at dilutes tea out of necessity and we are very careful to match the pH of the water to that of the tea to.mitigate those problems (for the record we dilute 10:1).
My personal theory is that the tea is an inoculant, and any little few drops will have millions of living organisms and if you splash those drops on a place where they can live they will spread and grow on their own and, over time, deliver their goods to your roots