Antenna Hardware - The yagi antenna is suited to the novice builder but there are many types. Each satellite has an uplink and a downlink so it is necessary to have an antenna that will work on the downlink side for receiving and one for the uplink if you are transmitting to the satellite (Transmitting requires a licence - an amateur radio licence normally suffices fr most countries). Antennas have a gain associated with them that is related to the number of elements. Simply the greater the number of elements the greate the gain, however the more directional they become and the greater accuracy is needed. So a trade off between gain and beam width is required. Nominally a 3 element beam for 145Mhz (2m band) and a 7 element beam for 432MHz (70cms band) will suffice for most applications. Some satellites need a different type of antenna that has circular polarisation and these are helical to look at. The satNOGS helical design should be followed. A simple to build antenna can be sources from Nuxcomm 
Receiver - The RTL-SDR dongle used for the reciver is a broad band software defined receiver (SDR) that uses a common IC for the receiver and simple filtering. Its intended use is for TV, FM and DVB reception. It can be hacked, using the right drivers to be a very capable and cheap receiver. Fot further information see here. eBay will be able to offer you good value.