I'm definitely no expert (FTM, 6 week old) but I got both a cheapish small one without pockets off Amazon and a larger one with pockets. I only use the small cheap one which came with a £20 changing bag. When we're out, I cover the baby changing plastic shelf things in tissue for hygiene (although our local ones seem to have paper for this purpose much like the rolls at doctors surgeries), then put down her buggy blanket folded a few times under her head to provide padding followed by the changing matt.
I didn't like the idea of keeping nappies/wipes in a clutch type bag or changing matt because they won't hold the quantity I keep in the changing bag. That's just my preference as we go through so many and I risk forgetting to replenish my changing bag stock (I carry a full pack of wipes and up to 20 nappies in fear of running out).
I also tried to use a large bag (longchamp medium sized pilage one to provide context) because I didn't like the look of any bags I saw in shops at the start. However, quickly discovered the need for millions of pockets to quickly find dummies, wipes, nappies, formula, bottles & need for a separate waterproof pocket for new clean clothes if accidents occur/pocket for dirty stuff. I got one for £20 off Amazon to try with the vision of buying a better one if the changing bag trial worked and it's been pretty good & have ended up not needing to upgrade! Came with 2 changing bags (one normal size and one very small for if you're going out for an hour & just want 1/2 nappies) and another mini zip bag I use to keep dummies together inside their sterile container. On Amazon it's the second listing down when you search for "changing bag". I've seen quite a few mums out with this bag as it's so cheap but functional. Only thing I would say is it depends if you want to attach the bag to your pram. Ours is a bugaboo bee5 so can't hold a bag over the handle as it doesn't have any clips or bulk to stop a changing bag slipping down so I keep the bag under the buggy on the storage shelf so it made no odds if it fitted onto the buggy. I actually prefer this set up now as there's no bag hitting off me/the buggy as we walk & I have a clear view of baby.
I am now looking at getting a backpack style bag but this is purely because baby feeds on the 200ml premade bottles of formula when we're out so I end up carrying half filled bottles around. The lids on them are rubbish and tend to leak if it kept totally upright & due to the changing bag being on its side under the buggy, have had a few leaks.
Sorry for the long winded answer but all in all the cheapy Amazon changing bag with the matt it comes with has served us well! I looked at the £100 bags in mothercare at the start and am so glad I didn't go for one of them.