To the OP: I know you've already chosen and ordered your DE razor (great choice BTW) but I thought I'd chime in here anyway in case there were others that were still pondering their own DE purchase.
You really can't go wrong with Edwin Jagger IMO. Their gear is top notch, they've got something in a price point for everyone, it comes from Sheffield (knife knuts know that generally means quality), and from my personal correspondence with the folks at EJ HQ I would feel comfortable saying that the customer service is also top notch. I have also heard good things about Merkurs but haven't used one myself. A year or two ago I bought an Edwin Jagger Chatsworth in Barely Chrome, with matching Silver Tip brush in Barley Chrome and a chrome EJ razor/brush stand. It came in a three piece set from the Edwin Jagger website (I did just check and it looks like they no longer offer this set, unfortunately) and was stupid expensive--over $400 CDN when everything was said and done. That being said I would not trade it for anything. Like a good custom knife it is a solidly made, elegantly presented tool that will last generations with the proper care and use. Not to mention that wet shaving pays for itself very quickly, due to the money you save not buying expensive disposable cartridges, as others have already stated.
Some general points about buying a DE razor that others have already touched on which I feel compelled to throw my two cents in on as well, for whatever reason:
- Weight and Length are key. Ideally it would be best to handle any razor before you buy it to make sure that it feels right in your hand. That is an idealized scenario however so in reality there need to be some guidelines. IME/IMO length is the more subjective option: some like their handle longer while others like it shorter. Personally I like something in the middle or a little on the long side but of course different things work for different folks. Weight is a totally different ball game however. IME/IMO the more weight that a DE has (within a reasonable limit) the better: I would personally stay away from anything that has a plastic or composite handle. A heavier DE just shaves better...and for that fact you can thank physics
- Blade selection is very important, and trying a variety of razor blades is a great idea to get a feel for what works for you...but as others have mentioned there definitely IS a technique so you don't want to try too many different types of blades or soaps too quickly. Try something basic like the Astra Platinums that have been recommended by many and shave with that until you've got the technique down and then you can experiment with blades. As others have hinted, I would recommend staying away from Derby blades: they had a great reputation many years ago but like too many things in this world it seems like their QC is gone down the crapper and now you'll get some excellent shavers and some duds in a pack. I personally love Feather Hi-Stainless Black blades (black refers to the packaging colour, not the blade colour) but also realize that they won't work for everyone and they are wicked sharp and unforgiving so probably not a great choice for beginners.
- Soap selection cannot be over emphasized: IME/IMO the soap you use is a just as important as the blade you choose, and both of those decisions trump the DE razor selection itself. Someone who knows how to use a DE razor can get a good shave with a crappy DE as long as it's fitted with a good sharp blade and they're using a quality, high glycerine soap. That is my opinion of course and I'm sure others will disagree. Personally I use Castle Forbes, and while it may be one of the priciest brands going the shave it enables is very, very smooth and it produces so much lather that I only use a TINY drop whenever I need to shave. Again, this stuff goes such a long way when used appropriately that you will definitely be saving money in comparison to cheaper soaps and creams.
- If you find you are really into wet shaving then at some point down the road I recommend buying a shaving scuttle. Certainly not a necessary addition but it takes the whole experience up a level and IMO once you've used one you won't want to shave without one. I strongly recommend Schwarzweisskeramik scuttles but there are certainly other worthy brands out there if you do some research.
A final word of warning: if you are a knife knut getting in to wet shaving...beware. It will not be long until you start coveting expensive straight razors like Thiers Issards and Dovos! Can't beat a straight razor, as long as you know how to use it
EDIT:
To the OP: I just read the last few messages (which I had missed previously). As others have mentioned it is more than likely your technique, but that Derby sure isn't helping. A dull blade can be seriously dangerous to shave with--IMO a dull razor is more dangerous than a sharp razor, if you are using them properly: dull razor blades have propensity to snag...not something you want to happen while you're shaving your neck or the like. It's far too easy to jerk your hand and make a sideways motion resulting in a niceee little (or not so little) gash on your face. I would change out the Derbys for the Astras (or the Personnas--never used these personally but they seem to be well liked so I'll have to try some!) and then keep doing what you're doing. The technique will work itself out with time and practice. A really good tip (best one I ever got when I was staring out) is to not use too much pressure: let the weight of the DE do the work--if you're shaving at the right angle slight pressure and steady motion is all it should take! Finally I see you're using a hot water wash for your face, and that's certainly great. While this may be obvious I think it also bears mentioning: even better than a hot washcloth is taking a hot shower before you shave. This really opens up your pores and helps the hairs just slide off your face. If you find you're still having trouble once you get your technique down then you should try a pre shave oil or a cream. I can personally recommend Musgo Real but I know there are many others people have success with as well.