If you are on a budget, you won't get top spec. But for 350 you can get something equivalent to what was top spec a few short years ago.
Solid state memory is way faster, but for the money much smaller. For example at the lower end of budgets, you might only get 128GB solid state memory, but 500 GB of disk memory. Unless you are a power user (gaming etc) you probably will not notice the speed difference that much, but if you download a lot of video 128GB will fill up fast. Remember that a HD movie can be several GB now.
Screens are much higher resolution and easier to read than they used to be. 15.5 inch is great for visibility now.
If you go to the big retailers you can sometimes buy what they call refurbished. This is a new computer that may have only been out of the box once before being returned, but cannot be sold as new. They come with a full guarantee, and big price reduction.
Brands. All the major brands are pretty solid. Computers are pretty reliable nowadays. If you travel or are heavy handed with stuff, the Lenovo ThinkPad are robust. The rest of the Lenovo range have less expensive casings than many other laptops, and this is reflected in the price. Lenovo are a Chinese company that bought IBM's computer manufacturing.
Go the the retailer, see what is on offer, then Google the reviews. I don't usually understand too much about the tech reviews, but the star ratings give me some confidence in purchasing choice. Lemons are rare, but the reviews will find them out.