Building your own is better and cheaper. It's also the easiest part about a rig. Getting it working and maintaining it is much harder. There is lots of information on this board and elsewhere that will help you find out what you need. The basics are a motherboard that is known to support the number of GPU's you want to use. There are many options here. Dedicated mining motherboards like the ASRock H81 BTC Pro, Biostar TB85 and Biostar TB250-BTC and TB350-BTC are good options but hard to find unless you want to pay a premium. Other boards that work well are the ASUS PRIME Z270-A / AR which support up to 9 GPU's using M.2 to PCI-E adapters.
The next items you need are CPU and RAM that supports the socket type of the motherboard. Common sockets are Intel LGA 1150 with DDR3 RAM and LGA 1151 with DDR4 RAM. All you need is a basic processor, no need to go for more expensive options and 4GB of RAM is enough. It's a good idea to check the motherboard manufacturer's website to make sure the CPU and RAM models are on the recommended list to use with the motherboard. For a hard drive most go with a 120 GB SSD with Windows, again a basic model from a good brand is all you need. If you want to run smOS, a good USB 3.0 flash drive is another option.
The PSU is the most important factor in a rig. If your PSU goes down, at best so does your whole rig and at worse it could damage equipment. You need a good quality gold or better rated PSU that can handle the load and has enough PCI-E and Sata connectors for the cards and Risers. Good options are EVGA and Corsair.
For ETH and ETC mining, AMD RX 4XX/5XX cards have better performance and dual mining capability compared to Nvidia options that are more expensive. The problem is finding multiple AMD cards without getting gouged is very hard ATM. For Equihash mining, the Nvidia 1070 or 1080 is a good option if it's not much more than a 1070. Scrypt mining like LTC, was taken over by ASIC's years ago and can no longer be mined profitably using GPU's.
For risers I recommend going with 6-pin PCI-E risers. They use three thicker wires made to handle a higher draw and four capacitors for a more stable currrent flow compared to the 3 capacitors and thinner wires used by Sata or Molex risers. The 6-pin risers also use a voltage regulator to prevent spikes.
For a case I recommend building your own using the BBT mining case below out of two 8ft pieces of 1/8" x 3/4" angled aluminum, one 8 ft 1" x 3" piece of pine and #8 1/2" self-tapping screws. The case will fit up to 7 RX 4XX/5XX if you put them about 1 inch apart. The cost of the aluminum angles and screws was ~$35. If you build it out of all wood, the cost would be less than $10. That's a much better design that allows for good airflow.
https://www.youtube.com/watch?v=D5xNrlxsCVs
The only tools needed were a drill with a 3/32" hex titanium drill bit to drill pilot holes and a #2 phillips screwdriver bit. A hacksaw with a 32 tooth blade and a plastic miter box to cut the aluminum and wood. The case is very sturdy and can support up to 7 GPU's.
BBT also recently uploaded a case build video with a smaller form factor for a four card rig:
https://www.youtube.com/watch?v=8n9tgRw_JkMThe benefit of the previous case is it would give you room to expand in the future. Though I would also suggest making the case 1.5" taller from 9 1/4" cuts to 10 3/4" cuts to give you more clearance when using USB risers.
