if you want to play Blu-rays on your console, you need a Xbox One S. PS4 can't play physical Blu-rays, they can only stream such content.
with $400, you could buy both consoles if shopping properly. just get the 500 GB version of each, as you can add external hard drives later on. just looking now, the consoles alone the PS4 slim at best buy is $230. and a standalone Xbox One S is $190 on sale. look to see what games you have on Xbox that are backwards compatible. you should already have Xbox Live Gold, so you don't need to buy it again. just sign into your same account, and you'll be good to go. BC on xbox one is also free. you just need to own the games.
PS4 does not have pure BC, but since you don't have any games, you'll have to pay for that service if you did anyway. it's a pure streaming service, and it's $99 a year, along with the standard $60 for PS Plus online play, like Xbox Live Gold.
one thing you can do now to start is start using Microsoft Bing, their search engine. along with Edge, their browser, they have a rewards system for using their products. you can earn around 300 points a day or so from searching alone, and one of the rewards they have is Xbox Live Gold. 12 months of Gold is 30,000 points. if you search every day between PC and mobile app, you can earn 12 months of Gold in around three months. if done for a year, you can earn three years of gold. then just save the codes for when you want to use them, or use them all at once, as you can stack the on your account, and they'll run consecutively. you can only add up to three years total of Gold on one account anyway. then save your money for PS Plus and other games.
CDKeys.com is one site to look for for less than retail value prices for PS Plus or other digital gaming accessories and games. you could try eBay, but you risk getting scammed there.
it mainly comes down to what exclusives you want to play. if you want to play Halo, get a Xbox One. if you want to play Uncharted, get a PS4. each has more exclusives, so you need to do some research and see which one has more you want to play.
i would also keep your Xbox 360. look at what games you have, and what games are backwards compatible on Xbox One. not every game may come to BC in the future. that's up to the publisher. and even if MS gets the chance, they may not release it if they're having porting issues. so keep the 360 if you want to play your games.