Dont want to sound pessimistic, but 100k is a real tight budget for a complete PA systems.
- Behringer Eurolive series - Active speakers only. You would not want to get a passive one (without amplifier) and add the trouble of power amps, cables, setting it up etc. The B208, B210 are the ones you should look for. They come in a very good casing which will protect it even when abused. For other wodden made ones you would have to make a casing additonally which will eat away your budget. For a amphitheatre, 2 active speakers, above 250rms should be good, though it will not please you a lot, but then the budget

. I had couple of events with these in a 3600 sqft closed area (office cafeteria) and they blow away your ears, without compromise on sound quality. These are real bang for money - 19k each, onwards. Peavey and JBL (similar casing stuffs) are other options but they cost high. I guess these speakers dont come with a stand, so another 5-15k on two speakers stands.
- Cabling - pretty much all are same unless you want to build a home studio. You would need a lot of them. Park aside 10K.
- Mic - Shure SM58 and Shure SM57 for vocals (speach & music) and works well with instruments. @ Re 3800 each. Cables additional. These are very good for a band performance as well as speach. Very sturdy as well. Beware there are ample duplicates of these which a normal person wouldn't even be able to differenciate. Search youtube for the differenciation. Mic stands @ 1.5k each, onwards. All the brands are pretty much same, unless you are going for instrument specific mic stands.
- Lapel mics - Would be good only for speach but for plays, I doubt. They are not omni directional. So the actor has to speak straight to the mic for him/her to be heard. That collides with the acting part

The actor would appear as suffering from spondylitis

. My take, get a good omnidirectional mic with a overhead stand. I dont have too much knowledge on this.
- For live music performance you would need atleast 3-4 mics. Electronic instruments will have their jacks. If there are accoustic drum sets, then anyway you would need a professional to tune all the mics to the drums, so keep that aside.
- Mixer - Ah! for band / plays you would need atleast 8 channel mixer. Since your speakers are active, get a unpowered mixer. Again Behringer is a good option. Yamaha also has some good ones @ 22-25k range. I personally would not prefer Ahuja / pulz mixers for they are too 'raw', you know what I mean. Basic functions like echo / delay / phase / tone control is more than enough.
Excluded: Stands for mixer, power sockets etc.
Disclaimer: I personally dont own any of these equipments, but I have used them a lot. I dont intend to advertise for any company/brand either.