My suggestion would be to buy second hand. Very rarely, you may end up with a sale going on, where you can pick up a set of Ben Hogans for about 150-200 (they are good clubs). The thing with clubs are that different people prefer different types of clubs, depending on their build, their height, their flexibility, and subsequently, their swing.
The ideal way to go about buying clubs would be to first show up at a big store, and try out the clubs in the store. They usually have try out rooms with simulators where you can take shots with taped up clubs. Once you are comfortable with a certain model/models, check out the used market for those clubs, or older generations of the same model. 90% of the time, the older generations of the clubs will be very similar to the one you tried out, but on some occasions, they will be different. You should be able to tell.
I, for example have a set of Mizuno MX-17s, which are an older generation to the Mizuno MX-19s. The 19s had just come out when I bought them, so I was able to compare both 19s and 17s in the shop, as both were still on sale at the time. I preferred the 17s to the 19s because they were heavier (I'm not sure why I prefer heavier clubs, but they do suit me more). That is a rare case where an older generation of club will be very dissimilar to a newer generation club.
Anyway, you should go with what you feel. Buy the club that you feel suits you more, that you feel is easier to hit, rather than hunting for a brand name (whether it is used or new). Maybe you will find that the Adams suits you really well right now, so you may want to just buy those. The whole game is based on feel. If you feel comfortable, the clubs will work for you.
If you do decide to try out clubs in the store and purchase second hand, the key advice I can give you is that, as a beginner, you want to look at cavity back clubs, rather than blades. Cavity back clubs are a lot more forgiving, for beginners, and do not accentuate the flaws in your swing. The other type of club is called a blade, and those are clubs that do hit better, but only if you have a good swing, already. They are massively unforgiving, as, if you don't hit them well, your ball will go flying in every direction. Your draws will draw more, your fades will fade more, etc etc.
Good luck in your club hunt, and I look forward to checking out what you end up picking up.
Remember one thing, though, if you are picking up a set second hand, then you will probably end up having to purchase a set of irons separately, a driver/wood/hybrid separately, and a putter separately. Rarely will you find all of them in one set. So if your budget is under 400, I'd say spend about 200-300 on your irons, about 50-100 on a driver/wood/hybrid and 50-100 on a putter. You will find a lot of good stuff in that price range. If you end up spending less than 200-300 on your irons, my personal advice would be to look more carefully at putters than at drivers, or other long clubs, because, whereas a driver or a wood is usually your first & second shot), you wrap things up with your putter, and the fewer times you use that, the better. You don't want to putt more than twice, in a hole, right? Maximum thrice .