Rod preference is so personal. Great recommendations above. I say go cheap, you can get great starter rods/reels (Bass Pro, Cabellas) for under $100. I wouldn't worry about it - they will feel fine and give you great service.
In your situation I think it might be important to have at least two rods ... the issue with 7/8 wt rods for bass is not the size of the fish at all, a 3 weight line will easily handle a big bass (with appropriate leader, but the fly line and rod would do the job and I'm not recommending this ...), rather it is the bulk and size of the fly. I have shad imitations 4-5" long that simply have to be cast by my 8 weight. Even the 7 wt is a little awkward with them. I fish poppers and flys/streamers for gills and smallmouth all the time with both my 7 and 8. I also bust bluegills with my 5. My 5 is my main trout rod, though I like my 4 weight for brooktrout.
A great 2 rod start would be the 6 weight (the first post was spot on I think) - that will do it for any of your species using smaller flies for bass than maybe you will ultimately, and an 8 for the bigger stuff.
That said, I'd stay with the 6 and develop for a while before deciding what your rod array should look like.
I too soon started collecting rods and would have done it differently if I gave myself time. To wit: after a couple decades lay off I came back to the sport in VA. My first rod (replacement, my rods were lost in a move a ways back) was an 8 because I wanted to target smallmouth and largemouth bass, and wanted the flexibility to have a decent striper rod (had friends who loved to striper fish and there was a possibility of steelhead trips). I love that rod still. Then I found great trout fishing in VA and got excited about getting a trout rod. Jumped too soon, got a 5 wt, followed a few months later by a 4 wt. Then I won an Orvis 7 wt in a raffle.
What that left me with is too many rods. There's not enough difference to matter; I love the 8 for big river fishing, bass/pike. I do like the 5 for big trout fishing on VA's larger streams. I would prefer a 7 or 7-1/2 foot 3 wt for my mountain brook trout rod over the 4 wt I have now. I like fishing the 5 for the bigger rainbows and browns, many people prefer to stick with 4 wt. Some right where I live swear by their 7 wt for big brown trout. It's all a matter of personal preference built on experience and learning. My 7 wt (granted, it was a raffle win) is just superfluous.
So, if I'd let life and times guide me, I'd have spent much less money and I'd have a short 3 wt, a softer than what I have 5 wt, and my 8 wt, and I'd be in rod nirvana. I don't have the budget to redo anything, and I'm not dissatisfied with what I have, but I always recommend to newcomers that they slow down and learn to use and love one rod and a set of techniques and target fish first. Thas' just me.