This is my 2 cent opinion,
I belive 2m band (144Mhz) is good start point why :
1. the size of antena is "manageable"
2. the cost for accesories (LNA, down converter, Antenna switch, PA) is fair enough
3. The activity is among the EME enthusiats is good
I will not suggest to try EME with a wet string type station but many-many report with 12 element single yagis can made some 2 way contact and if You can not transmit cause You do not have licence maybe You can contact some "big gun station" like W5UN, DG9MAQ (germany), VK3GY(Australia) and many more to made schedule to try to listen to them.
if I start again from zero my EME station here list I like to have (remember this is a list for 2 way contact)
1. Decent HF transceiver like TS850, FT950, etc
2. Down converter (antenna mount style with LNA)
3. Low loss cable like heliax LDF5
4. 1Kw Solidstate PA
5. Antena switch relay with sequencer
6. 2 X 12 Element optimized yagis (K1FO etc or You can buy from cushcraft, M12 etc)
7. PC for sofware logging, Moon Position, cluster monitor)
seem many thing but honestly in my Country with almost 300 milion people there is no more than handfull people can hear their sound whats like after travel 600,000km away.