I think it is worth having the lightest walking boots you can get away with. The old adage of "a pound on your feet equals five pounds on your back" is very apt. However, I have the most comfy boots ever and they are heavy leather winter boots, so I don't follow my own advice!
Leather / Canvas
Some of the Coast Path is rugged and rocky, and often wet, so I'd recommend leather over canvas boots, but leather is heavier. If walking in summer, I'd definitely be looking to wear light weight canvas boots.
Buying from a shop
Getting correctly fitting boots is essential. You need to explain to the sales person what walking you intend doing. Then get your feet measured properly. Try on as many pairs as you can. A quality pair of boots is not cheap, but they should last for years. You may even find 2 pairs of exactly the same boots feel different so don't be afraid to be a nuisance.
Everybody expects walking boots to be fully waterproof but they never really are. If it is raining hard and a wind is blowing, it is not just the puddles and mud that will make your feet wet. Water will run down your legs and into your boots from the top. Breathability is the key. This is why Gortex linings are so popular. Of course, if it is hot then sweaty feet need to breath too!
Please don't assume that any old socks will do when you are taking on long distance walking. Blisters can stop you walking all together. They are caused by friction and moisture. Take advice at the hiking shop. Your socks need to give you cushioning, padding and the ability to wick moisture from your feet.
Drying out Kit
If you are at a B&B or hostel then ask if they have anywhere for you to dry out your wet boots, socks and other kit. If you are camping then you will have to put your wet clothes back on in the morning; not a very pleasant experience, I know, but you need to keep a dry set of clothes for the evening.