I will offer some advise. First off I have repaired and calibrated thousands of tools and gages, not just calipers, so hopefully I can help you out a little bit.
First off, I would also recommend a digital over a dial caliper. The reason is not readability. The dial calipers use a set of gears that contact the rack. These will eventually become clogged up (sawdust?) and make the caliper more difficult to use over time, I have seen some bad enough to skip teeth but that is rare. When you do not use the caliper, either keep it in the case or place it upside down (reading face toward the table) so dust cannot get into the moving parts. A digital caliper uses a magnetic strip with an encoder and does not have as many problems with dirt and dust. Usually the gib (dial and digital both have) just gets dirty.
Next, the repeatability of your measurements depends on a number of factors. Pressure, the thumb wheel on the base provides a means of applying pressure when taking a measurement. Typically for metalworking this would be light, enough that you would create a slight drag when moving the part around inside the jaws. There are specific numbers (in oz of force), but don't know off the top of my head. The end of the jaws have a knife edge, metal won't compress enough to cause a noticeable change on the caliper, but wood is soft and the knife edge could cause a change in reading.
From my experience, the gib screws on cheap hand tools are almost always too loose or too tight. The gib screws are the two on the top of the caliper. If you place one finger on the top where the gib screws are, and your thumb on the bottom (where the thumb wheel is) and rock the assembly against rack, you should feel no movement. If you do, give the gib screws a slight turn to tighten them up. The screws may also be so tight you cannot slide the caliper, or it could mean the caliper is just clogged with dirt. Either way, DO NOT REMOVE THE GIB SCREWS on a dial caliper. If you remove them and the gib comes out, you will loose tension on the hairspring and the caliper will not repeat a measurement. If you have never tightened a hairspring before, it is a royal pain, that and you need gage blocks to check for accuracy anyway. A very loose gib can cause the whole assembly to rock, causing the caliper to read off a little bit.
If you are measuring a flat surface, considering you are using the same amount of pressure and are not using the knife edge. If you rock the caliper a little bit, the lowest number will be the reversal point (the actual reading). On a curved outside point, the highest number will be the reversal point. On a curved, inside surface, the reversal point will be the highest number. A flat inside surface, the lowest number will be the reversal point.
Wood also has other little things that will change your measurement. Wood has a different surface texture. Metal work usually has specific roughness, or finish specifications. Wood usually is very rough and has grain that is not smooth. You may have a tough time seeing it, but most calipers are accurate to within 0.002 inch (+/- 0.001 inch). Dust, dirt and the grain will play huge factors.
What is the difference between a Harbor Freight tool and a quality Mitutoyo, Brown & Sharpe or Starrett? Well a number of things. I can take a five year old Mitutoyo caliper and check the linearity, step, depth and inside measuring surfaces and almost every check will be at nominal with one or two at 50% of it's tolerance. I take a tool from Harbor Freight, NSK or Fowler and most all of the measurements are at their limits. So in a few years time the caliper has to either be reworked or replaced because it has worn out of tolerance. The cheap tools often use soft metals that nick easily, making them more difficult to slide. The more expensive tools usually have anti-backlash mechanisms, etc.
For my money, Mitutoyo makes the best caliper. I like some of the older Starrett dial calipers, but they were never able to make a decent digital version. The earlier versions were plagued with electronic problems, and the new versions are just cheap. Starrett also uses an odd sized battery for the calipers that you cannot get at a department store. Starrett hardly makes any tools in the US anymore either. Typically is you see a "J" at the end of their model numbers, it stands for jeweled, and you will find higher quality parts inside (ie metal gears). The hard plastic cases are cheap and crack, the older cases used to be either soft plastic or wood. It is kinda sad, considering how many machinists buy their products because they are American, I hope they change their ways.
Hope I could help!