Quality always matters but sometimes it matters more than others. When you're taking up hiking it's easy to get sucked into buying gear that is more expensive than you need. Knowing when those extra bucks are worth it is important when you're just starting out.
Side note, you may want to check out our post What Hiking Gear Your Really Need
Boots are usually worth spending money on. No other single piece of equipment will impact your enjoyment as much as your boots. It's all about staying comfortable because comfort = happiness. Expect to spend at least $100-$130 for a good pair of boots. It pays to shop sales because these are generally bigger ticket items.
Read reviews, a lot of them, before purchasing any boots. Granted, not everyone will have the same foot type and that does have an impact on how comfortable they are but reviews will help you find the flaws. Is the stitching cheap? Are the soles too soft? That sort of thing.
To figure out if they are comfortable (at least initially) you want to make sure you're trying them on in store and walking around a bit in them. Just remember that if they aren't comfortable in the store they won't be comfortable outside the store.
Spend money on good hiking socks. An expensive pair of socks is under $20. Just to keep that in perspective if I asked you if you would pay $20 to get rid of blisters that developed on your feet after a day hike, you would probably pay it. Given that those expensive socks often have lifetime warranties, socks are one of those things that you should just pay more for because they are worth it for almost any level of hiker. Be sure to read up on preventing blisters while hiking.
Twenty bucks is nothing, it's the difference between taking a family to Papa Murphy's or Papa John's for dinner. Yes expensive socks are 3-4 times more expensive than regular ones but you're talking a difference of $15, it's worth it.
Poles are optional to get started hiking and you don't need to spend a lot of money on them, but don't go too cheap. Costco usually has trekking poles for sale in the spring and early summer, those are almost always a good deal. Look at the locking mechanism on cheap poles, if it's a twist lock and cheap you'll probably want to avoid them. When buying lesser known brand poles, which I recommend to save money, reviews are your friend.
Expect to spend around $45 or more on decent poles. Get them from Costco if you can.
Go cheap on your first backpack or get it at REI. Starting out hiking you have literally no idea what you want but a backpack is very person specific. I recommend buying it used, buying it at Costco, or buying it at REI (see warranty overview).
Costco: Good quality but cheaper than REI
REI: If you don't love it return it within a year, period.
All of these are good options because you probably don't know what you need and once you figure it out it's almost a certainty that it'll be something different than what you bought.
If you're day hiking don't worry about size much, anything above 20 liters is fine for day hikes and will force you to keep the extra junk (usually not needed) to a minimum. That being said, the Trail 40 Backpack from REI is hands down the best carry-on I have ever had.
Also read up on what features hiking backpacks have that you think you'll need. Check out our beginners guide to hiking backpacks as well.