You need to provide more information. What kinds of wines have you liked so far? Also, you need to define what you mean by non-expensive. For some people it's four or five bucks, for others it's under $15, and for others it's considerably higher. For me non-expensive is under $15, but if that's more than you want to pay, that's OK.

As a general rule, whites tend to be cheaper, although not always. Partly it's because they don't have to pay for expensive oak barrels in some cases, partly it's about demand.

Some of the best bargains in the market are rieslings from Germany. They are traditionally indicated as QBA, Kabinett, Spatlese, Auslese, etc. and the prices increase from left to right. The designation refers to how ripe the grapes are when picked, not necessarily how sweet the actual wine is. But you can find some like Schmitges Grey Slate, or Lietz Dragonstone, or Gunderloch Jean Baptiste and those are almost always under $15 and worth every penny. You can even find some for around $10 sometimes.

You may also look at some rose, or rosado. As we come to the end of summer, some distributors are lowering prices to clear their inventory and some stores are passing the savings. Many of those are sold by the grape variety they're made from, so if you like one, you can try the red version of that grape.

If you look at some wines from Australia, they have plenty of friendly, fruity, inexpensive wines. I'd stay away from things like Yellow Tail and whatever's on the shelf next to it, but moving away from that Yalumba, Lindemans, Jacob's Creek, Oxford Landing, Tyrells, Penfolds all make wine that's really not bad. Spain also has some really good values out but you need to look at what's in your area.

In the US, Chateau St Michelle in Washington produces some of the better values on the market. Their little brother Columbia Crest does too, but I think their whites are better than their reds. Try all of them -- they'll give you a pretty good idea of the grape type and if you like one or another, you can explore that particular grape.

Don't worry about pairing. IMHO, there are very few complete disasters. And many things are OK with many other things. For example, It's hard to think of a wine that doesn't go well with simple roast chicken. Whites, reds, rosado, sherry, almost everything works. Some better but none are disasters.

If you put some herbs on it or some fruit then you change the dish slightly and help define which wine you should be drinking.

If the dish doesn't seem to work well, that's OK. Just eat some of the food, chat for a while, and sip the wine. Don't mix them in your mouth and you're OK. You'll know for sure when you've got a good match because you'll just stop in your tracks to enjoy it.

Last night I had lamb and I made a mint chimichurri with scallions and lime. That would kill most wines and kind of killed the wine I selected but hey, you live and learn.

A nice Rose' might be a good answer as well. Try Monte's Cherub 2008 nice easy drinker but still has the umph of a light red,
http://www.snooth.com/wine/montes-cherub-rose-2008/
Or Francis Coppola's Sophia Rose'.
http://www.winechateau.com/sku11065.html?utm_source=Shopzilla&utm_medium=feed&utm_campaign=FRANCIS%20COPPOLA%20SOFIA%20ROSE%202008

Both delicious easy drinkers and will be a nice segue into other fuller bodied wines.

I think the Menage a Trois blends from Folie a Deux are always very pleasant to drink and are around $10 they make a red, white and rose. Some people that I know have tried them who are new to wine have liked them. They are a little sweet, but not overly sweet and maintain the characteristics of the grapes used to make them, so they can help you to start picking out scents and flavors. I would assume they are widely available too if we can get them here in PA! http://www.folieadeux.com

You might try Beaujolais, light, fruity and strawberry flavors, but totally dry. This is usually inexpensive, but stick to recent vintages (07 or 08). Another alternative is Cotes de Rhone from southern France.

Chenin Blanc, as was mentioned, is also a good choice. Aside from CA and WA, South Africa has some good ones (e.g. Ken Forrester), and from France there is Vouvray, which can be dry or off-dry.

For pinot noir, Fleur de California and the higher acid Lucas and Lewllen are good choices. From New Zealand, Matua and Crossings are two inexpensive ones I've liked. I am also fond of Elk Cove PN from Oregon.

Mad Housewife from CA has some good (to my taste) inexpensive wines. I like their Merlot.

My wife and I are always trying new wines. With 2 or 3 new ones, we will have a range of different foods arranged and try them with the wines, experimenting and remembering what happens.....good, bad or neutral. Some surprising food pairing have resulted. Often, the taste of the wine will change, depending on the food or spice that you introduce it to.

Our usual lineup of small dishes may include bread, olive oil, strawberries, goat or lamb's cheese, hard sharp cheese, brie, 80%+ dark chocolate, green peppers, sundried tomatoes, hummus, taboulleh. One of the pleasant surprises was a Pinot Gris from Washington that was refreshingly fruity upon first taste, but not overpowering. When pairing it with the hummus, WOW! That really opened the wine up, and it went really well with middle-eastern spiced lamb as well. You never know until you try it out. It is also a good way to use up those small amounts of leftovers in the fridge.