Welcome to the community Tom....
Straight line inlays like I believe your describing are arguably the easiest to do and can be accomplished a number of different ways. You could get away with a good straight edge (typically a metal ruler) as your guide. A thin sharp edged cutting tool. Could be anything from a box cutter to a scalpel. I really like using scalpels! And a nice sharp chisel. This process is labor intensive, but what you learn carries forward to other methods and techniques.
Use of a router plane is another option. And a very good one. I have the complete setup that Tom mentions above from Lee Valley (veritas). It is nothing less than a high quality tool! Capable of clean groves and smooth bottoms. Downside is cost and it is limited to pretty much straight line groves. A task that can be achieved by much less expensive means. The inlay cutter head is a VERY COOL option for their router plane. Takes a little getting use to but boy, does it do a nice job. Allowing for radius grooves this accessory is what sets this group of tools apart. Taking the design potentials to another level. More narrow channels/groves can be cleaned out using their inlay chisels, wider groves can be easily cleaned using good sharp shop chisels.
>>>>Veritas inlay tools<<<< Lee Valley Tools - Item Search Inlay Cutter Head for Veritas® Router Plane - Lee Valley Tools
I also have several of the Lie-Nielsen inlay tools. All high quality tools!!! None of em cheap though. https://www.lie-nielsen.com/search?q=inlay
In all fairness, very few of the high dollar tools accomplish anything that can't be done with much less expensive means. Convenience and ease of setup, accuracy and repeatably is what tends to set them apart from other tools. That and the fact that they are just simply a pleasure to have and to use. Personally I most of the Veritas stuff and find it all excellent.
If a router is what you feel comfortable with, I'd suggest the Bosch Colt with the plunge base option. Plenty of power for inlay work, limited to 1/4" shank bits. Small enough to be easily manipulated yet big enough to not feel flimsy in your hands. Easily controlled/guided over the work piece. Visibility of where the bit meets the wood is fair to midlin as is the case with most small routers. While doing inlays, chip extraction isn't too big of a deal since most passes are shallow by nature. With a full line of accessories available including guides, more than enough power and adjustable this one is my favorite for inlay work. If you want a router that is a little more versatile (general shop use as well), the Dewalt DWP611PK compact router kit is well worth a long look.
Always take the time to size your banding/inlay to the tool you are using. Its not unusual to find straight inlays are undersized width wise. Cutting a 1/4" wide groove only to find that the inlay is 7/32" or less wide can be very annoying!!
Regardless of the method/technique used, PRECISE layout is a must. If you are looking for professional results you got to get your layouts spot on. Spend an afternoon or weekend practicing what it is your trying to accomplish. First couple of tries, use a soft wood, pine or better yet popular. Once you got a feel for what is going on and what to expect, try it on a piece of the wood you are going to be working with. The woods density/hardness/grain patterns all introduce little deviations into process that if unexpected will just create alot of unnecessary frustration. Some folks find that depending on the wood, scoring the cut prior to making a pass with a router lends itself to a much sharper/cleaner edge. The cleaner the cut, the better the inlay will look. Sharp tools are a must as are precise layouts. IMHO straight line inlay is not all that difficult with a little practice. The devil is in the details though. There are ALOT of good quality video's out there on "how-to". Including youtube! Spend some time just watching the variations on a theme. I can almost guarantee you that when you get that first piece just the way you want it, you'll be hooked on inlays and what they can add to a project. And it only gets better from there...simple string inlay work, well done can take a project from ordinary to extraordinary with just a little extra work. I realize this is all kinda vague and all over the place, but there is an awful lot of ground to be covered in a short post. Once you get started, post your questions and concerns. There are alot of top shelf wood workers in here that will be more than willing to help you along..