Cheap braid would result in more tangles and more problems. .
Are you going to get a Baitcaster or a Spinning reel?
If spinning then 4 or 6lb Berkley Fireline is quite good value, on traceme 300yds can be gotten for around $50. That’s enough to fill a Shimano 2500 reel twice (With a little backing). If you reverse the line at the end of the season then 300yds should last 4 years.
For a baitcaster, maybe give Powerpro braid a try. It is $52 for 300yds
Most braids overtest something amazingly, very few braids would break beneath 10lb. I know that 4lb fireline breaks between 10-12lb.