I have about 7 pair of calipers, Brown and Sharp, Mitotoyo, and some cheap ones. The cheap ones have been relegated to the woodshop where I don’t need precise measurements. I find that if I am on a budget, I will look for dial calipers. Yes, they are a little harder to read and generally only one unit scale, but they also don’t need batteries. I have one 4 inch digital Mitutoyo that I use for precision work and the rest are dials for price, simplicity, and durability. I have only had to send one pair in for work.
I also found that with a little scouting, eBay is a good place to get used ones. If you find the right set, they have been carefully used and loved and are just as good as a new set.
I also have one pair with carbide inserts in the teeth for metal work so that I can scribe without dulling the jaws.
EBay is good for deals, but man am I ever tired of buying things on there that have flaws that should have been listed in the description!
The second-to-last set of calipers I bought was from eBay. Got a pretty good deal, but when it arrived it had some serious flaws. First, they wouldn’t power-on while the battery cover was put on (being able to turn them on is sorta important) and the PCB was so loose the measurement would shift 9-thousandths just from PCB movement (making them worth approximately nothing).
I took them apart and found that some dillweed had taken them apart before me and only managed to put back two of the four screws. The four screws were in a rectangular pattern, and the last person to take them apart somehow decided to put both screws on one side, leaving the other side screwless. I put the two screws on opposite corners and it seems to hold OK. I really need to try to find some matching screws before I forget. I also cleaned up the battery contacts.
The calipers seem to work OK now. I complained to the seller and they refunded me a little more than 20%, making the final price about 1/3 of what Amazon was charging for a new set.
I splurged on the real Mitutoyo and am very happy with them. They have heft and have held up very well over the past year. I can’t imagine doing laser work without something like this. I use them all the time and they still look and function great. The one tool besides a Glowforge you are absolutely going to need if you are departing from Proofgrade and ready made designs.
I have a set of all plastic general and a $35 or so metal generic. The generals are a bit flakey but work, the generic ones work great but are only 3 significant digits. To me, Mitutoyo is overkill but I’d never fault anyone for wanting or haveing them. I’d like to get something in the $75-100 range for my third pair. Recommendations?
I bought a couple of the cheap ones about 10 years ago and was happy with them but they wore out. They became sloppy and developed a fault where they would jump 0.2". I bought a couple of cheap replacements that looked the same but over the intervening time I think the quality has gone down. They skipped 0.2" when new and had all the problems described in this video https://www.youtube.com/watch?v=WvszAb0Y0Ec
I binned them and got two Mitutoyu expensive ones and they are so much better. So I think ten years ago I would have recommended the cheap ones if you don’t need great precision but now I think there has been a race to the bottom and the cheap ones are rubbish.
I just ordered these from Amazon: http://amzn.to/2qImOJV
I’m sure they’ll be fine as a starter. I’ve never used calipers before so will probably be totally gobsmacked by their beauty and accuracy! 
I still have my dial calipers from 20+ years ago! Still 100% accurate and have never had to change the batteries 
I’ve bought a dozen of these off Amazon in the past couple of years and only had one fail to zero properly.
I use them for my basic laser class and students typically don’t have any background with digital calipers so they don’t always treat them extra carefully 
I’ve also got a set from Lowe’s at about 4X the price (I paid something like $8 or $10 for the Amazon ones last summer when I last bought a set - watch the price, sales are not uncommon) and except for the logo couldn’t tell the difference.
Here’s another area where my ignorance of laser cutting is slightly mitigated by being in the jewelry business and having plenty of calipers : )
I bought a $150 one 25 years ago form a jeweler’s supply, I was bucks-up at that point and was enthralled by the first digital calipers I ever saw. It was just a splurge at the time, and had only been lightly used - until 
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6" dual scale +/- 0.0005 silky smooth operation and heavy.
No way to shut off, so I pull the battery when not in use, and still using the original button cell!
I agree with @Hirudin, on a quality tool. Never be afraid to buy the best, you will always be happy with it.
Edit; this coming from a guy who has spent plenty @ harbor freight 
I have a couple cheapos (and a pack of half a dozen plastic vernier calipers that are good enough for many measurements) and a Mitutoyo that someone gave me as a gift. The cheapos mostly work fine, but the battery life (if you leave the battery in) is really annoying. I go down to the shop after a couple months and pick up the cheapo caliper to measure something, and the battery is dead. I keep thinking I should hack in a switch…
In that range look at Brown and Sharpe dials instead of digital. If you want digital, be prepared to pay at least 125 for a 6 inch set.
This is where eBay may be worth looking.
I have a few, the ones I bought for myself are http://amzn.to/2pZhj6M. I believe they are quite a good value for the money. The USB cable costs significantly more than the calipers. 
The Amazon “Stainless Steel Digital Caliper” looks a lot like Harbor Freight’s version too. The price is about the same, maybe a little less at HF. I have one and it has held up OK, though I find I need to remove the battery between uses to keep it from draining.
Shar’s Aventor brand of imports are pretty decent and come with certifications (whatever that may be worth from China). They come in 6", 8", and 12" lengths and the 6", which I have, run around $45 and have been working well and accurately for me so far. Calibration checks against known good standards are right on the mark.
http://www.shars.com/products/measuring/caliper?brand=Aventor
The HF I had exhibited some slop - I could wiggle the rear jaw head. The Amazons don’t have that slop. Mine are all auto-shutoff and the batteries seem to last a yearish. I used to turn them off but let them just do it themselves now. I’d never go to the trouble of pulling the battery - I’d trash it first.
I’m using the cheap harbor freight ones, a 4" and a 6" Model. I have tried them on standards blocks, and they check out well enough. You do need to zero them every couple of measurements, or before you take a critical measurement.
Buying cheaper calipers allows me to buy multiples, so I can have one on the lathe, in the woodshop, and in the office.
I think I bought a 50 pack of LR44s on Amazon for $5.
I know there are considerable differences in battery life expectancy of LR44 vs SR44 (latter being longer), so keep that in mind when shopping for replacement batteries. However, the cheaper calipers use more energy when off than higher quality ones (to maintain position…essentially they’re always on but the display is either on or off).
So I got a pair of the plastic ones to play with as at £3.58 delivered there is nothing to lose.
Measuring a machinist’s block and comparing with Mitutoyo calipers and micrometer with 1um resolution I get the following:
10.0 10.07 10.076
20.0 20.09 20.088
40.0 40.06 too big
So, not too shabby considering the price, but not very accurate. They do make my block look spot on though, so a bit like looking through rose tinted spectacles. It reminds me of the first time I saw digital signals on a 100MHz scope at university. I previously looked at TTL signals on a 100kHz scope I made myself while at school and it made square waves look perfect. I was horrified to see how bad they are in real life.
An advantage of the plastic calipers is I can use them to measure features on my computer screen without scratching it.