Do you actually need 12v at 1A for fans? You can buy computer fans (120mm or 140mm with lots of airflow) that only need around 0.15-0.35A to work just fine.
Alternatively, if you're going to use a 18v AC transformer why not just use a 24v fan? Just like 12v fans which are designed to tolerate up to 13v, the 24v fans should work at up to 26-27v just fine.
Your 18v AC transformer will be rectified to 18v x 1.414 - 2 x ~ 0.7v = ~24v ( PEAK voltage, the minimum voltage will depend on how much capacitance you're willing to add) and even with +/- 2v due to mains voltage variation, the fan (or fans) should be fine.
Digikey has plenty of them, for example here's a 24v @ 0.08A max 92mm fan for 7$ : https://www.digikey.com/product-detail/en/nmb-technologies-corporation/3610SB-05W-B50-B00/P15567-ND/3594465
It feels like it's expensive at 7$, but if it saves you 1-2$ for the 12v switching regulator, your cost is only around 5$ ... still more than a cheap 120mm 12v fan, but a quality 12v fan with so much air flow will be close to 5$ as well.
So the fan is 12v to 27.6v DC , 0.08A (1.8 watts), up to 3050 rpm and produces up to 54 CFM ... very efficient fan moving lots of air and you can run it straight from input voltage. Connected straight to the output of the transformer (after bridge rectifier and capacitors) it will see a input voltage around 18v to 26v depending on how much capacitance you have and how much the other rails take... either way you'd still have plenty of air flow over the heatsink.
Oh.. and keep in mind that you could also use this fan and everything in your "product" with a laptop adapter style power supply which has a default 16.5v to 19v .. usually 18.5v. The fan would still run quite fast from this voltage, and the voltage is still high enough that a ldo would output a cleaner 15v for the opamps and so on...
You'll have a peak voltage of 24-26v and you say you need 15v at 100mA and 5v at 3a (15w) and 3.3v at 300mA (1w). Assuming 90% efficiency that means you're going to need about 1.2w for 3.3v and about 18w for 5v, so overall about 20 watts.
So let's say we want a minimum input voltage of 18v and let's work with peak voltage of 22v (for situations when your mains voltage will be slightly less than 110v AC so your output is less than 18v ac) .. then for 20 watts you'd need 20w/18v = about 1.15 A so you should maybe put enough capacitance for around 1.5A of current..
C = Current / [ 2 x mains frequency x (vpeak -vdc min)] = 1.5 A / [2 x 60 hz x (22v-18v) ] = 1.5A / 480 = 0.003125 Farads or minimum 3125 uF ... so I'd probably suggest going with a 3300uF or maybe a 4700uF or 2 x 2200uF 35v DC rated capacitors, at least (use more than 3125uF if you want higher minimum voltage all the time).
Now that you know your minimum dc voltage will be at least 18v and at most around 28v, for just 100mA at 15v you won't get much higher efficiency with a switching regulator compared to just using a linear regulator.
So for the 15v 100mA, i'd just use a ldo like this one for example : https://www.digikey.com/product-detail/en/on-semiconductor/MC78M15CDTG/MC78M15CDTGOS-ND/1481487
DPAK makes it nice heat dissipation wise and at 0.4$ it's cheap. It has a 2v dropdown voltage at 0.5A, much less at just 100mA ...
So 18v in , 15v out at 100mA is an efficiency of around 84%, with 22v in it would be around 70% - a switching regulator may cost 2-3$ and give you 85-90% efficiency but at only 100mA you'd only save something like 0.1w to 1 watt (in worst case scenario with 22-24v in and 15v out). Rather than spending 2-3$ on a switching regulator, spend an extra dollar on a higher VA rating transformer if needed.
For the high current 5v it makes sense to use switching regulators to get the better efficiency.
You could buy ready made POL dc-dc converters (for a one off or just a few pieces it makes sense) or you could make your own switching regulator.
So yeah.. you'd probably need a 35VA rated transformer to get your voltages at those currents you want. A 35VA 18v AC transformer has about 2A ac current, or about 0.62xIac = 1.25A dc current, which is slightly more than what you need.
ps. Thinking about it, you probably wouldn't need a switching regulator for 3.3v at 300mA ... that's only 3.3v x 0.3 = 1 watt. You can just use a linear regulator to get 3.3v from 5v, so instead of designing a 5v 3A switching regulator, design one for 5v at 3.5 A or slightly more.
5v in at 0.3A , 3.3v at 0.3A .. that's 66% efficiency and about 0.5w loss. A switching regulator will give you 95% efficiency and only about 0.1-0.2w loss but is it really worth spending 1-2$ more to save 0.5 watts? Not really...
//edit : i don't know why i read 3.3v @ 3A so i did the numbers assuming 10w for 3.3v ... edited to correct it.