Welcome to the forum, I am pretty new also, so I can relate to the burn.. I started about a month ago and just the last week or so have been burn free, so stick with it, you will learn the angles, pressure, prep / routine. Once I started pulling my face the correct direction for my trouble areas is when things got better. A sharp razor is key also

As for budget, the b/s/t section here is great. You can always message one of the sellers and let them know you are new and on a budget to find out if they have anything they can recommend in your price range. Keep the purchases simple, a razor and a strop is really all you need to get started.