The price of the stroller DOES matter (to some extent - as well as later on)
TL;DR: A stroller too budget-friendly may cost you your time & nerves. Go for quality, better (not necessarily most expensive) brands and models, and watch out for no-brand cheap stuff. It's for you as well as the most precious person in your life, after all.
I know - me too - we DO love bargains. The better the price, the more accessible and not too guilty the purchase feels. And with a stroller, stroller system, pram, pushchair, or even a simple buggy - one of the more expensive pieces of baby gear... the money to pay is considerable, even with those rather affordable models. And I know and understand not everyone wants/can spend a lot. I never could either.
However, I somehow came to get extensive experience with strollers and their functionality, and the first thing I want your mind to accept is this. Most probably, you are going to use this piece of gear pretty much EVERY DAY. Often more times a day. And! It's going to carry and provide comfort and protection to the most precious thing in your life, your innocent little fragile baby. This is certainly not to say you need to buy the most expensive thing you can find, not by far... But I do want to say that there should be 'functionality over price' thinking right from the beginning. Not the "I don't really want to spend much on such a thing as a stroller," I heard this several times (and it always ended up badly).
Imagine the stroller, please, being similar to your cell phone you take out of your pocket so many times a day - or like your notebook, if you work online - or as an operator for a taxi driver. Yeah, you CAN survive it with something simple, not much of quality, and not too comfortable... but that is why the better phones (and better employees) always win in the end (and in the long run). 'The occasional' can be lower-quality, but your 'everyday helper' (which a stroller certainly is) needs to work well and reliably.
Think of this. If a pushchair is crazy cheap, even if looking good on the picture or the promo video... they HAD TO get to that low price somehow. They had to economize - and use lower-quality materials (plastics, joints, less thick tubes more prone to breakage, lower quality wheels or their tires - which can mean rattling or worse driveability, thin fabrics that can tear or fade quickly...). The range of places to save up on is quite wide, and any of these changes to the worse you will be feeling when using the stroller.
Lastly, I want to draw your attention to another important thing. When you're done with your stroller (system), most probably, you will want to resell it. That's a great thing that is economical for your family, but also it's very ecological to reuse, recycle, upcycle even. Some strollers can truly be like new - after changing the wheels for new ones and buying a color pack to change the look a bit. Look at how it works in the personal ads. The good stuff is always gone or too expensive to be worth buying a used one. The cheap stuff is all over classified ads websites, and no one wants it. A more expensive model of a well-known, popular brand (and popular means it's good - otherwise, people wouldn't like it) will be sold so much easier. In the end, you'll have paid pretty much the same price for a "luxury-priced" (or at least a more expensive, high quality) stroller as for a cheap model of an unknown brand. The no-brand model you will end up giving to somebody that desperately needs it or sell for almost nothing (if it doesn't break in the meantime).
Again, I am not suggesting buying absolutely anything that's expensive. I am trying to suggest to you not to be overly thrifty and, in the end, lose money (and your sanity) because of saving money in the first place. Your time and energy are also worth money, do you know? ;-)
Do your research, check what stroller models are long-lasting, which prams well-reviewed, which pushchairs asked for in buy&sell groups (like some on Facebook), which buggies a long time present on the market... and try to find a price compromise. And yes, if you need something affordable, go for those in the lower price ranges within what came out well from your research - but not lower.