MCU selection for developing a baby monitor
When a "simple" antenna transmits power, that power tends to spread out in most directions getting "thinner" as the distance from the transmit antenna increases. By "getting thinner" I mean that if you could catch and measure all the power passing through a 1 sq metre square "dish" you'd find that power falls off with distance squared. This is the basic theory behind "link loss" and the ability to formulate the number of dBs of loss between transmit antenna and receiving antenna. Of course it's more complex than this around a house or from a base station to a cellphone but the principle will help you understand the importance the transmit frequency.

Link Loss (dB) = 32.5 + 20\$log_{10}\$(F) + 20\$log_{10}\$(d) 

where F is MHz and d is distance between the two antennas (kilometres). 

At 2.5 GHz and at a distance of 100 metres (0.1km) the loss is 32.5 dB + 68 dB - 20 dB = 80.5 dB.

If your transmitter were operating at 1 GHz the link loss would be 72.5 dB. If operating at 434 MHz (a common UK standard), the link loss would be 65.2 dB.

All these frequencies are OK for getting through a house (and the various obstacles presented) so I'd tend to go for the lower frequency if that is available to use in your country.

At the receiver end, the smaller the data rate the more sensitive the receiver can be. A well-trodden formula that predicts how much power a receiver needs is this: -

Power required in dBm is -154dBm + 10\$log_{10}\$(data rate) dBm

At 100 kbpsec the power needed is -104dBm but at 1 kbpsec this improves to -124 dBm.

So, choosing the lowest data rate you can at the lowest transmission frequency available is a good starting point. If you used 2.5 GHz and 100 kbpsec, the receiver needs 35.3 dB more power to be transmitted compared to 434 MHz and 1 kbpsec (all other things being equal).

What about the CC2530? It is specified as needing -97 dBm typically and this is likely because it operates at 250 kbpsec so I'd ask myself - do I need a transceiver or can I make do with a transmitter/sender and a receiver/bracelet (halving complexity). I googled 433.92MHz receivers and this one needs only -109 dBm at 2.5 kbpsec and takes a power supply current of 3 mA. This is a lot less than the 20+ mA needed by the CC2530 and importantly, if the bracelet receiver has to last a long time on battery then you should be thinking about this too. 

I'd be considering adding a very low power MCU to this type of receiver and waking the receiver up once every ten seconds for a quick "sniff" of the ether to see if there was potentially a transmission coming from the transmitter.