Been using a safety razor for years. The handle will be more expensive up front (around $30 on Amazon I think), but the blades after that will be dirt cheap. It's definitely much more of an art than disposable razors are. My suggestions would be:
1) get a good handle. Butterfly open to secure the blade is common. Make sure it's stainless. If you can apply adjustable pressure to the blade to change the angle it meets the skin, that can be helpful.
2) know you will cut yourself more at first. The blades can be wicked sharp depending on the brand you get. You'll have to teach yourself how to keep tight skin under the blade and not apply probably as much pressure to the blade as you're currently used to. Let the blade do the cutting on its own.
3) Astra blades are cheap and rather sharp off Amazon.
4) learn how to actually shave. One pass will make you presentable, but you'll do better if you think of going in three stages on any area. With the grain, across the grain, and finally against the grain in that order. Reapply cream or lubricant as needed.
5) speaking of cream, look into cremo shave cream. Imo works better than traditional gel or cream, but other people hate it.
6) a good after shave balm like Nivea can help relieve shaving burn that will likely happen early on.
7) done correctly, a safety razor will give you a much closer shave. If you really want to step it up, look into straight razor handles that use the same blades. Those are much harder to master on keeping a good angle to your skin though.