Hi!
We had a timeshare there for 10 years and took our baby-then toddler before 'it' ran out and we would definitely recommend it.
It isn't commercialised as the Canaries. It has a micro-climate - warm all year round but further into the mountains is can be cooler and even in summer, at the highest point you would need a cardigan!
Hotels: Porto Bay and Pestana are the biggest chain.
Porto Bay have: Porto Mare Residence, Porto Mare Hotel and Eden Mar which are technically in a C shape and all connected despite being 'different' hotels. It is situated about a 25 minute walk out of Funchal centre but they have a courtesy bus regularly to take you into town and back. I would walk in then get the bus back. But buses and taxis are cheap. The hotel chain is right next to the Lido and the main tourist hotel spot. Lots of restaurants, the promenade can be accessed all the way to Camara De Lobos which we walked with our then 7 month old in a baby carrier (August!) Lovely fish restaurant there.
There is also Cliff Bay which is 5 star Porto Bay hotel and half way along the road to Funchal.
Both are suited to families. The 3-hotel chain have a creche which is stocked well. You ask for the key and use it at your leisure, a small playground below in the herb garden (they are well known for their gardens) and they have 3 main pools (1 is 1.5m in depth, the other is deeper at one end, indoor and a toddler pool). Cliff Bay have an indoor and outdoor pool, access to the sea and some toddler toys outside near the main pool.
Pestana is also a firm favourite with families. We have had a week at Pestana Promenade when it first opened. Very modern but slightly lacking for small children BUT they have several other hotels on the island. Google them.
The Savoy is nice. We went for a look round and we were impressed and lots of families.
I can't recommend it enough. Though we don't holiday there anymore, we plan to when the children are older.
It's ideal for a young family with babies/toddlers and maybe older teens who are happy to muck about the pool, listen to music on loungers etc.
We have a nearly 6 year old (the one we took to Madeira) and a nearly 3 year old and we're holidaying at the bog-standard resorts catered for families with slides etc - for the time being!