The Shaveology razor is either a re-branded Edwin Jagger DE86, or (more likely, but hard to tell from the photos) one of the many South Asian clones of that razor. It's as good a place as any to start.

The notion that you can't use a DE razor with canned shave cream is just silly. It's what most guys did for most of the 20th century.

I'd venture to say that your primary mistake wasn't using Barbasol, but assuming that you can use a DE the same way you can use a cartridge. In fact, there's a bit of a learning curve involved. Be patient in figuring out your blade angle, and use no pressure while you're doing so, and you should be able to get a close, comfortable shave.

That said, a lather made with traditional cream or soap will likely improve the quality of your shaves. All soaps and creams do the same thing - you use a brush to mix them with water and air and use them to shave. A good one will be slick, provide cushion, condition your skin, and smell nice.

The only major difference between creams, soft soaps, and hard soaps is how difficult it is to get some on your brush. With a cream, you can just dip the tips of the bristles in the jar and go to town. A hard soap may require some vigorous swirling to load enough product to shave with. A soft soap will be somewhere in between.

I like the variety and quality of artisan soft soaps that are out there. They tend to perform better than mass-market stuff (eg, Proraso, Cella) while being less expensive than the high-end brands (eg, Castle Forbes, L'Occitane).

So check out Maggard Razors artisan soap collection. Snag a jar of something that sounds good to you (maybe Mickey Lee's The Kraken or Maggard's London Barbershop, or Barrister & Mann's Cheshire, but there are dozens of good options). Pick up a brush while you're at it - the Omega S-Brush synthetics are very inexpensive and have been getting good reviews. A blade sampler can't hurt, either - you'll be surprised how much difference the right blade will make.

Then spend some time in the FAQ on the sidebar. Watch videos. Make practice lathers. Work on getting your angle and pressure right. And enjoy!