I would see if you can find something that can be adjusted in size, so you get enough use out of it. Also, it might be best to get something you can try on in an actual shop as different harnesses fit different dogs differently, if that makes sense I'm sure that others will suggest actual brands that they've been happy with.
I used cheap mesh harnesses off Amazon when my last pup was little and changed to a fleece backed harness from Dog Games(online) and the a Perfect Fit harness when he was pretty much grown.
My two were on Puppia mesh harnesses when they were little. They are really broad across the chest, so no chance of them digging in when the puppy has one of its manic moments. I got them with plenty of "wriggle room" and they lasted from about 15 weeks to about 7 months!
I used a back fastening harness but then moved on to the Happy at Heel side fastening harness, best thing I ever did was stop using the back fastening harness as I couldn't always stop as soon as he pulled. After two months he is now on a collar and lead, I could have moved over sooner as he improved so quickly. My OH uses the Perfect Fit harness as he could stop if Dexter pulled. It is also about training with whichever you choose, being consistent is key. If I did it all again I'd probably stick with a collar and lead from the outset but due to shoulder surgery 3 weeks after getting our boy I couldn't put a collar on him but could put on a harness.
