I had the Tiger Combo from Wal Mart years ago and thought it was a great starter combo back then. The rod lasted a long time, but the reel only lasted a couple of years in the salt environment. It might not be the same as yours though.
When I first used braid I bought 20lb line because that is what we used in Florida in mono mostly. When I got it, I thought that this dental floss isn't going to hold anything. Man was I suprised, I pulled in all the fish I hooked up, including salt water species. I went both ways back then because I lived in the middle of the state, sort of.
My heavy rods are older, whuppin sticks which are like the old Eglass ugly sticks, They have 6000 Penn Spinnfishers on them. I have never put more than 30lb mono, or 40lb braid with 40lb mono backing on em.
For shark, and casting heavy weights, I used an 80lb mono abraision leader about 12foot long, and then a steel bite leader about a foot long. I was usually pier fishing, so I didn't need to cast it too far.
You would be amazed how big a fish you can bring in with lighter line, if you work them in. And how much better lighter line casts over the heavier stuff, even if its braid.
Another thing is that a heavy rod usually takes quite a bit of weight to cast any distance, mine won't toss anything worth a flip until I have 4 ounces on it.
Keep in mind I'm just throwing out things to think about, what you use is your final decision and what you feel most comfortable about.