Your budget constraints are tough to work with. If you can extend that up to the $30. - $40.00 range, your odds go up dramatically. The Pflueger Trion in small to medium size will work just fine. And the 7' rod would be ideal for your purpose. Take a look at the BPS Micro-lite series - decent rods at reasonable prices. You should be able to find something there that would fit the bill.
As far as long casts are concerned, the line has a lot to do with it. You might want to look at a good "fused" line (not a braid) with a fluorocarbon leader. The fused lines (like 4# test Fireline) will allow greater casting distance than any mono can hope for and the fluoro leader will give you the abrasion resistance that you need on the business end. Join the two with the Alberto knot and you're good to go. Good Luck and let us know how you make out.