I'm not seeing the issue with the mobile data if no wi-fi is present?!? That's how they all work. If you have a smartphone, you certainly shouldn't be on such a small data plan. These things are designed to suck data. That's their purpose.
As for signal, that's a harder part. The number of bars can be tricky as different manufacturers program their phones differently. One phone can show one bar and still be stellar and a different phone from the same manufacturer or a different manufacturer can have all the bars but still suck. Now, when it drops from something like LTE to Edge, that's a different story.
When I am at my parents' place, their house is a bit of weird place for reception for me with any phone. There's one spot that can be temperamental. The Note 3 is a tad more so than my Note 2 but still better than previous phones like my Nexus One and GNex.
I suspect you're paying more than $75 for this phone. I'm on Tmo and I certainly know it. Do I think it is worth it? Yes. It's probably one of the best smartphones out there right now. To make the best use of it though, I would look into a better data plan because that's what these things are about. They should be hooked up the network and pulling data. If I am only going to be on wifi all the time, well that's what my tablet and laptop are for.