You don't say what size you have now. I will take a guess that your rod is small.
For most land based fishing in river and lakes etc...I would suggest an 8 foot rod with a 40 size thread line reel.
First the rod. Shakespeare Ugly Stick is very good. If you look after it, it will last you a life time. The ugly stick is affordable for most people. If you want to get something a little cheaper here is a couple of things to look for. The guides (that is the round things the line goes through) look for Fuji. Then hold your hand vertical so that your thumb is pointing up, place the butt end of the rod on your ringer just in front of the hand grips. Then with your other hand reach up as far as you can towards the tip of the rod. Then rock the rod back and forth so the it rolls side to side on your finger. You will feel a bump or click. This is called the spine. You want the guides to line up very close to the spine. You want a medium action rod. This will be marked on the rod as fast, medium or slow. Action, is about the tapper of the rod and to complex to explain here. But it basically means how fast the rod goes from thick at the butt end to thin at the tip end...called tapper and referred to as action. Medium action is a good all rounder.
So to sum up on the rod...I would suggest an 8 foot medium action Ugly Stick...Or a cheaper brand with Fuji guides.
The reel... You can't go past Shimano. There are lots of brands and types but Shimano is a very popular brand and they are very good. You want a thread line reel some times called an egg beater. The numbers for the size are simple, the bigger the number the bigger the reel. 40 size is good for an 8 foot rod. It might be marked 4000 but it makes no difference if it is called 40 or 4000, it is the same thing. Put the reel on the rod before you buy it. I know you wont know what to look for but it should feel "balanced". Try a 60 size reel also. If you go into a tackle shop, they will have no issues in letting you try different combinations.
http://www.shimanofish.com.au/products/fishing-reels/spinning/ix-r.html
This link shows you the Shimano IX R 4000. Entry level no bearings graphite construction...perfect. It might be a little light on an 8 foot rod, so you might want to go with a 6 or 7 foot rod. But this reel is very good to get you started. I use the IX R 4000 on an 8 foot graphite rod. (oh, yeah, don't go looking at graphite rods just yet. get a few years under your belt first). No bearings is a bonus. These reels use brass bushes. All graphite casing and spool. In short this reel is tough as nails, wont rust, wont cease up, is smooth and easy to use and has a quick release bail arm for one handed casting. On top of all that, the IX range is entry level, so it is not expensive. The 2500 is about $25 Aust. Not sure what the 4000 costs, I have one but don't remember what I paid for it.