Recommendations for Budget Shoes?

What others have already suggested--going to a store that specializes in running--and taking a few mins to figure out what you need is the best option. From there, the previous generation or two of shoes that fit your needs can offer great cost savings.

All that being said, if you are just looking for a quick answer / run of the mill shoe, that is a good value I'll throw out:

Nike Pegasus 39; A workhorse of a shoe that will take a lot of miles before you have to replace
Saucony Triumph or Saucony Kinvara which are, for me, a bit more comfortable but not quite as hard wearing

I want to try the shoe fit thing on a store, but I'm just worried the people there isn't actually knowledgeable and would just upsell me stuff.
- The stores I buy from have pretty open return policies if the shoes don't work. Fleet Feet, for example, has like sixty days or something? I ran about fifty miles in a pair from them before I had to admit that they were too tight. They accepted them back and refunded me in full, and when I asked what happens to the pair of shoes, they told me it just gets donated.
  
  This is all a long way of saying that if you can find a shop with a generous return policy then you can expect that their to priority will be to get you in a shoe that works. (Of course this might just be an option in USA.)
- If you go to a dedicated running store they’ll typically be very knowledgeable and want to help. If you go to a footlocker or champs style store they are trying to hit their sales goals, there is a difference (though not always true in every case). I would suggest going to a local running store and being clear with your intentions

With the $150 budget you mention in the comments you are honestly not really on a budget that restricts anything. It really depends on what specifically you are looking for.

But in general if you are looking at good value running shoes: the puma velocity nitro and Reebok floatride energy are two good daily trainer options that are usually on the cheaper side. Beyond that you can honestly find most shoes, especially last years models on discount if you wait a bit and loom for deals. Saucony for example has quite regular discounts in the US. The difference between the ride 15 and 16 is minimal, so that could also be a good daily trainer option on discount

I was in the same boat not too long ago and I'm very much a beginner. The little research I did led me to believe the best option was to go to a store specializing in running equipment and talk to one of the knowledgeable salespeople there. They were able to tell me about what types of shoes would work well for me and help prevent injuries. They didn't have anything in my price range at the time so I went looking for the previous years' models of the same shoes and was able to get a good deal. Happily running ever since.

There is definitely nothing wrong with last year's models on the bargain rack (except maybe the colour scheme) as long as they fit right and feel comfortable. Don't bother with anything that doesn't feel really comfortable from the moment you put them on. I also second the suggestion for finding a store with a knowledgeable sales person as the fit might be a bit different from your regular shoes (often a bit larger so you have plenty of room in the toe).

Ones that work.

It sounds dismissive, but there's no point in buying shoes that turn out to be a poor fit for your feet or gait then having to buy more pairs. I paid a bit more up front for my first pair of serious shoes because I had them fitted in a shop, but since then I know I can buy the end of last season's stock on discount because they do fit.

Everyone's feet are different, so trying a bunch and picking your favorite from a store is probably the best way to go. I wouldnt buy shoes for running unless i had tried them on first.

Bonus shill: love my vibram five fingers

I will be trying out shoes, I just wanted to thin the heard a bit with the community's suggestions.
- TLDR: need more info from you
  
  I'm not sure you're going to "thin the herd" with advice from online randos
  
  Vibram five fingers is super minimalist, and i'm sure someone else is going to come in and recommend a 39mm max stack cushioned sole
  
  Shoes are so personal, it's really hard for random strangers to narrow down for you if you dont have a general direction in mind. You're going to have to provide more info on what your goals are.
  
  The reality is you might have try a few different shoes long term (ie, not just 15mins on the shop) and you might get it wrong for a few hundred km
  
  For example, i spent many years running on minimalist shoes (not super minimal/barefoot style, but like 10mm or less)
  
  Maybe it was right for me at the time, but i've moved on to max stack cushioned shoes for marathoning now. In hindsight, i think it was crazy for me to have run marathons at an older age in minimalist shoes
  
  I think a lot of people end up using multiple shoes for different types of training runs. So there's really not "one shoe" to rule them all if you're planning on doing a LOT of mileage and training

Probably easiest to start with your price range. Also if you know anything about your feet or shoes preference (like pronation, heel drop, toe box size, etc) it’ll go a loooong way, since what might be comfy for one person might be a pain for someone else

Price Range is probably ~150usd

How can I measure those shoe preference criteria you have mentioned?
- I think you’re above budget range at that amount
- As others have said, you can have a massive range of excellent daily trainers to pick from in the price range. I'll throw out a recommendation, Saucony Ride 15. Great shoe and you'll find it at a low price at the moment as the 16 is out. They didn't change much going from 15 to 16 either.
- Things like pronation (do you feet roll in or out), arch height is probably something a speciality running store can figure out if you’re not sure. Toe box (width around the toes), heel drop (how much cushioning is below your heel) is a matter of preference for the most part.
  
  All that said, they’re $160, but I really like the Fresh Foam X 1080v12 from new balance.

When I go to a running shop, when we start talking about actual shoes, I say, "I'm on a budget.". The sales people respect what my budget is, and if we can't get into the price range I need, they have always been courteous in telling me that. They want customers to feel welcome coming back.

BTW, in the US, Brooks online has a liberal return policy.