What do you mean by "tangent sights?" If you mean a blade or post front and a notch rear, set the big orange bull on top of the front sight flanked by the notch, flat across the top. If you mean the peep sights from the original picture, punch a circular hole near the center of the orange bull or paste a round black sticker near the center. The punched hole / sticker should appear slightly smaller than the front peep sight circle at your shooting distance. A punched hole / round sticker will also help with blade and notch iron sights as the smaller your aim point the smaller your groups will be. Always focus on your front sight, let the target and rear sight fuzz a little. It is impossible to focus at three different distances at the same time.
Make sure all sight elements are securely attached and do not wiggle. Also make certain the barreled action will not wiggle in the stock. I assume you inspected the barrel bore before you bought the gun. If you didn't, remove the bolt and make sure the bore is bright and shiny with no signs of rust or corrosion. Also make sure the grooves have nice sharp edges. This is also a good time to give the bore a good cleaning. Always work from the chamber to the muzzle with a one piece cleaning rod. It is OK to go back and forth sparingly with a brass brush as long as the rod allows it to rotate with the grooves. Use solvent or gun oil. I like Rem oil. Always push patches from the chamber to the muzzle and allow the rod to rotate. Also inspect the muzzle for any dings or dents on the bore edge.
When testing for accuracy always load each cartridge one at a time. It gives you and the gun time to cool between shots. Always remember the fundamentals: establish your sight picture, take a breath and exhale a tiny bit, then squeeze the trigger.
Be sure to keep those slide top CCI boxes. They are very handy when you buy cardboard boxed ammo. Also any lead bullet cartridge that falls on the ground or is carried loose in a pocket becomes a bore grinder, Do Not Shoot It.
If you can receive directly shipped ammo in your state, http://www.cheaperthandirt.com
has quite a selection of 22 long rifle ammo at fairly reasonable prices and any order over $99 is free shipping. Not sure how they do on sales tax as I haven't ordered from them yet. My shopping list has thirteen types of 22 l.r. ammo, most at less than ten cents a bang.