Both double edge and straight edge razors are going to require some learning curve over disposable cartridge razors. You will find people in both camps, and it is a matter of what works for them. Straights require some prep and upkeep. You will need one that is honed properly, you will need a strop to keep the edge, and it requires some prep work. But once you have a setup and learn how to use them, they can provide very close shaves. If you have the time and discipline to use one correctly it is a fine way to shave.
Double edge razors require less prep and upkeep, and blades are inexpensive. They do have some learning curve as well, however, as they have a fixed head and blade angle will be unique for them all. They can, however, be cost savers. I like them far better than disposables and get great shaves from them.
A third option is a Shavette, which operates much like a straight but uses disposable DE blades. People can tend to feel strongly for or against them. They are not true straights, but they are my favorite way to shave as they don't require the upkeep of a straight.
I am not as well versed as many here on straights and will leave recommendations there to the better educated.
As far as DE razors are concerned, there are many that will work well for you depending on your preference. Are you into or wanting to get into soaps, brushes, etc? That's a whole other rabbit hole of recommendations. If you currently are using canned creams or gels and want to stay with them, that's cool too. Some of my favorite razors are vintage razors that can be had online at fair prices. The Gillette Tech and Super Speed are pretty mild and can be had cheap. A few bucks more will get you an adjustable such as a Slim or Fat Boy that allow you to adjust the aggressiveness of the razor to your preference.
If you want new, I have had good experiences with the Merkur 34c (though it is a very mild razor) and the RazoRock German 37 slant. Both are very fairly priced, with the RazoRock being a bit cheaper.
If you want to go the Shavette route, $13 or so will get you a Magic Shavette, and it will take any standard DE blade, broken in half. It's my personal favorite shaving tool.
All that said, you have to find what works for you: your cost point, the time you have to devote to it, etc. All can do the job, you just have to determine which is the best fit. And I didn't even get into single edge safety razors, which also offer many good options and great shaves. They use a bit heavier blade, and are fun to use.
Enjoy the journey!
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