The problem with electrics and multi bladed razors is that they pull the hair to cut it. Pull it enough times before cutting it and it is short enough to fall under the skin causing ingrown hairs.
A DE razor may help because it only has one blade so it limits the pull to cut. I would say its worth a try for you and you can get set up with a good DE system for very little money, but there is a learning curve to get close shaves.
I have 7 razors and I paid a total of $100 for all of them, 2 were given to me, I bought 4 at flea markets, one I bought on a online buy and sell, and my first I bought from an online dealer. I know that is 8 razors, but I sold one because I didn't like how it shaved for me. so I got $20 back bringing my razor investment down to $80.
Blades would be the next thing to look at. To give a little price comparison, the last blade purchase I made cost me under $27 for 100 blades delivered. I get 4-5 good shaves out of a blade, a package of the latest and greatest multi blades cost upwards of $25 around here, and I would get maybe a month, a month and a half out of them
Picking a good soap/cream really helps too, and as the previous poster mentioned, prep is everything. If you don't take the time to ready your face its going to be rough no mater what type of razor you use. Even switching over to a quality shaving soap from the regular canned goo makes a difference.
If you do decide to switch over to DE shaving watch some of
mantic59's youtube videos. He presents well, and gives solid information. It will shorten the learning curve considerably. He is also a member here that steps in to check on us from time to time.
Things you have to watch out for with traditional wet shaving are
- RAD: Razor Acquisition Disorder
- SSAD: Shave Soap Acquisition Disorder
- SBAD: Shave Brush Acquisition Disorder
- ASAD: Aftershave Acquisition Disorder
- RBAD: Razor Blade Acquisition Disorder
Not that they are bad things, but your bathroom becomes cluttered as you acquire more stuff.
On an end note I have not had a single ingrown hair since switching to DE shaving and I can count the number of nicks I have had on one hand. So don't think of an old style double edge razor and something that is going to rip your face off. If you use it right you will have enjoyable shaves.