Welcome to iMore. Have a look at Spigen, Zagg, Otterbox or Tech Armor. All good screen protectors, but not necessarily cheap. I personally have always used Spigen and found them to be the best as they seem to offer the same feel as the actual phone screen. Many others prefer Zagg. Have a look and see if any of the brands I suggested to you suits your needs.
I saw a YouTube video that recommended the Tzumi ProGlass. I bought it the other day and I am pleased. I found it at Walmart for $9.88. Comes with an installation applicator that you put your phone in so the sp is straight. No halo effect at all. I'm gonna go pick up a couple more for backups.
I bought the Seidio Vitreo when it when on sale last week here at iMore. It's a glass screen protector and I am thrilled with it. Easy installation and it came with a $20 Uber ride credit!
I use inskin edge to edge tempered glass protector, it's excellent! Premium feel all the time. And it covers the whole front of the screen for about $12
I know this may not be the answer you're looking for in terms of cheap, but the Apple Store is installing the Belkin Invisiglass screen shields and their anti-glare one for $35 and $18, respectively. I like it because they have a device that aligns the protector perfectly and doesn't get lint caught underneath. To me, that's worth extra.
A screen protector preference is going to vary from user to user. I, myself, prefer Zagg. Yeah, I spend a bit more money, but the free replacements are worth it to me. Some like the cheap route that are easy to replace. More power to ya!