Much of this depends on the sort of rings you want and what sort of engraving you want. My first suggestion is to find the rings (plain bands perhaps?) you like. When you go to the jewelry store, ask if they do engraving. Ask if they do "inside ring engraving" if that is what you want.
Engraving on the outside is another option. Ask what kind of engraving service they offer. Very few will offer "hand engraving", that is, the sort of deeper and fancier work done when each letter or symbol is cut by hand using a tool called a graver. At the store I used to work with, the engraver there was only one of 4 who did that old fashioned craftsmanship in my state. As for pricing, hand engraving might be $120 when machine work might be only $20 or so.
Machine engraving is often charged by the letter after a minimum charge is met. To find the rings, you simply have to shop around. I suggest 14k as the minimum. This quality of gold is durable, much better overall than 10k and less expensive than 18k. If for some reason you prefer sterling silver, keep in mind that silver will wear more quickly and be more difficult to keep shiny and polished.
Silver will also tarnish for some people. Other kinds of jewelry you might see at lower prices are gold filled and gold plated. Also, there is something called vermeil. Gold filled is made like a coin, such as a "quarter 24 cents" and a look at the side of a quarter will explain it all. See the shiny surface of the coin? Look at the edge and you will see a darker, coppery colored layer. Gold filled is a layer of gold on top of another metal.
The under layer is a brass like metal and it will tarnish. Once the ring wears through the gold layer, there is nothing to do but trash it. It cannot be salvaged. Gold plated is brass like metal with an even thinner gold layer. Think costume jewelry for this.
Vermeil is sterling silver with very thin gold plating on the surface. Vermeil cannot be repaired or resized since any work will remove the very thin gold layer and what is left is a sterling silver ring with no gold color. Sterling is a lower cost approach than 14k gold but the rings cannot be sized if the ring has an "anti tarnish" coating like rhodium plating. Plain sterling is best if you choose this good looking "but subject to regular cleaning" metal. That is up to you! Ask before purchasing sterling if the ring has a plated surface like rhodium.
If the clerk has no idea what you are talking about, you might try somewhere else. Your question is general and I can give only general directions. But I do have an idea where you are coming from. Shopping for this kind of stuff is not easy if you have not done it before. These are some things to consider overall: Ask the jewelry store if they clean and examine your jewelry for free (the most basic of services). Try to get an idea of the services the store offers.
Most should offer that. It costs them little to do cleaning for a customer and makes for repeat business. Ask if they back up their service (repair work). Ask if the engraving is done "in house" or is farmed out to someone else. Actually, farming out work is not uncommon and does not mean a black mark for the jewelry store.
They SHOULD have a jeweler who repairs and sizes rings working in the store. A jeweler should be on the premises, even if they farm out the engraving work. Try to get an overall impression of the store staff, looking for people who are actually interested in your business and who seem to know what they are talking about. Generally the attitudes and knowledge of the sales people are a direct reflection of management and the approach of that store to doing business.
Are they happy to have helped you even if you did NOT make a purchase? Would you go back to them? Look for clues like this and try to get a feel for the way the store treats the customer. The customer is not always right, meaning, look for honesty and clear help when you ask questions about jewelry and about any services they offer. Ask if they do machine engraving or have access to hand work.
Machine engraving is like that done at the little shops set up in malls selling and engraving things like charms. A mechanical machine is used to duplicate the shapes of letters on master templates and scratch those shapes into the jewelry. Machine engraving is just fine and done correctly will look great and last a long time without wearing off. Hand work is different and is cut much more deeply, lasting a lifetime.
Each piece of hand work will show the ability of the engraver so if you opt for that; ask to see some samples first! As for the jewelry itself, you simply have to shop around and see the weights, thickness, etc. of the jewelry and compare prices from one place to the other. Look for a good finish on the surface of the rings. Avoid any that show little pits or marks.
This might be hard to see without a very close look. If for some chance you want white gold that is simply gold with another metal like nickel added to make the color whiter than yellow gold. The karat is more important than the color.
Go for 14k to start. That is my recommendation for wear-ability and quality combined. If you look at the much more expensive platinum, keep in mind that platinum does not keep a shine like gold does. Platinum is an excellent jewelry metal but because of the character of the metal, it does tend to get dull rather quickly. A high shine on platinum is difficult to attain and simply will not stay that highly polished as does gold (regardless of the color of the gold).
Victor Epand is the owner of http://www.JewerlyGift.biz, a huge online jewelry superstore featuring the greatest selection of jewelry including personalizable items. Clearance Sale items are here: http://www.jewelrygift.biz/collection/clearance-sales.html .