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I am not a fan of the Merkur 25c. The shave is fairly inefficient and the fit and finish are mediocre. The 985 is the same head on a travel handle.
The Parker 99R is somewhat more efficient, but IMO it's still marginal. And the price is too high - Parker razors used to be an economical alternative to Merkur and Edwin Jagger; now they generally cost more.
The Muhle R102 is the notorious R41 with a white plastic handle. It is probably the most demanding on the market. If your technique is not perfect, you will likely have irritation; bloodshed is a distinct possibility.
The Edwin Jagger DE89 and Muhle R89 (and R106, and R108, and...) are essentially the same razor; only the handles differ. I highly recommend any of them, especially if you can get one for $20-25.
Blades - You don't need to try 25 different blades, but you do need at least a couple of each to get started. Get a double or triple helping of the Top Ten Sampler from Try a Blade instead. More total blades (30 vs. 25), a good variety, three of each, and a lower cost ($9-12 shipped vs. $15).
Razor - The 34c is a decent starter razor. Fit and finish are somewhat sloppy on all Merkur products; if that's important to you consider an Edwin Jagger instead. The 34c does have the advantage of being a 2-piece razor, which is less likely to break if you drop it. For the best of both worlds, a Muhle R89 Twist is a 2-piece razor that's made to very tight tolerances and beautifully finished. Just be sure to buy it from an EU vendor - they cost nearly twice as much in the US.
Alum - Unnecessary and ridiculously overpriced.
Another good option is one of the starters kits from Maggard Razors or Stirling Soaps that others have mentioned. The VdH boar brush can be iffy in quality, and their soap is just "meh." You could upgrade both of those and get a pretty good razor and a small blade sampler, all for the price of the razor you're looking at now. If you really want one, both vendors sell alum blocks for <$5, too.
Sounds like the razor head you tried had too much blade exposure and/or too little blade angle. If you're willing to give it another shot, try the Edwin Jagger razor handle -- I'd suggest this one or maybe this one if you want more knurling for grip. They developed this new head design together with Mühle to be very forgiving for beginners yet still effective enough to satisfy old hands.
I use a knurled-handle Mühle variant that I love, but the head is the same regardless of which Jagger/Mühle handle style you choose. BTW, they also have an open-comb head variant that has the same blade angle but more aggressive blade exposure for dense/coarse whiskers, but sounds like you'd want to steer clear of that.
The usual safety razor advice applies: don't apply any pressure against your skin, don't grasp the handle, and don't go for long swaths; rather, hold the handle by your fingertips, let the weight of the razor head maintain light, gliding contact with your skin, and use short, overlapping passes.