I got the Relion from Walmart when I was first diagnosed pre-D. My doc later was able to prescribe me a different one, and strips, but I started out on the Relion. It works, and isn't that expensive, even as strips go.
Checking your blood "1 or 2 times a day" isn't all that helpful, unless you check it in the context of fasting or eating.
Taking your BG when you first wake up, before you eat anything, gives you your Fasting Blood Glucose, or FBG. This is helpful to see whether you're creeping up into pre-D territory (above 100 and below 125) or into D territory (above 125).
Post Prandial (after meals), or PP
The other helpful reading is the post-prandial, or after-meal reading. You eat your meal, and you take your BG reading at one hour and two hours after you began eating. This shows how your blood sugar reacts to the food you're eating. At one hour it may still be quite elevated, but by two hours it should be back down. You're aiming for a 1 hour PP of less than 140 and a 2 hour PP of less than 120. If you get higher than that, your body is reacting strongly to the carbs (starches and sugars) in your meal, and you may want to cut back on them.
Personally, when I was diagnosed, I tested mostly breakfasts at first, so I could build a repertoire of "safe" meals (since I mostly eat the same 5 or 6 things for breakfast). Then I ate my safe breakfasts and began testing lunches. Once I had a bunch of safe lunches, too, I worked on testing dinners. They're the hardest because there's SO much variety, and we eat fast food a lot!
Over time, I now have a mental list of foods and meals that I can eat that I know won't spike me above 140. In fact, most don't move me above 120 or so, but that's because I'm fairly low carb.
Using this method allows you to build your safe repertoire of meals, and only use 2 strips a day (3 if you do FBG, too). After a while, you may only test your FBG once a week or so, and only test at 2 hours after a new meal, just to see that you're still on course.
I highly recommend Blood Sugar 101, especially the section "How to lower your blood sugar". It completely changed how I look at food. The site has a LOT of great info (including explanations of studies that have come out and she explains them in laymen's terms).