20W * 24hr/day = 480 Wh/day used by the electronics
480 Wh/day ÷ 0.95 inverter efficiency = 505.26 Wh/day
505.26 Wh/day ÷ 12V nominal system voltage = 42.11 Ah/day required
Battery should not be discharged past 50%: 42.11 Ah/day ÷ 0.5 = 84.22 Ah/day
You need enough battery for 1 day at least, but typically we design for 2-3 days of autonomy for those times in the winter that the solar is not available. How critical this system is will determine this number. I will use 2 DoA for now: 84.22 Ah/day * 2 DoA = 168.44 Ah
At this point some people will add a factor to account for a little breathing room and possible future expansion. I will give it 10% here, but you will know what you nee din yyour system: 168.44 Ah * 1.10 factor = 185.25 Ah battery bank required
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As for the solar, i do not know your area or any details so I will use general numbers
505.26 Wh/day required to be replaced in the batteries each day (from above)
505.26 Wh/day ÷ 0.80 battery charging efficiency = 631.58 Wh/day required from solar
I would need to know your area and what time of year you plan to use the system to work out the irradiance, but essentially you need to know your Peak Sun Hours for the worst time of year you plan to use this, usually winter solstice. I will use 3.5 PSH as that should cover most areas: 631.58 Wh/day ÷ 3.5 PSH = 180.45 W PV array required
180.45 W ÷ 0.77 system losses (incidence angle, soiling, wiring, etc) = 234.35W Array required
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So this is all rough math (leaves some details out) to give you something to play around with. What I am getting at is that the 110Ah battery might be on the small side. If this system is critical at all I would consider 3 DoA which would put you closer to a 280Ah battery, but I think 185 Ah would be sufficient if you dont mind the battery discharging below 50% here and there in the winter. The 100Ah would work. Most days you should be able to get the battery charged back up by the end of the day. Just keep in mind that there will be days you discharge below 50% and there may be some days in the winter that youhit LBCO.
As for teh solar I think 300W is appropriately sized and you should be good to go, but that depends on your area and if you need to keep this running through the winter. Considering how inexpensive PV is I would add more.
The inverter I can not help much with as I typically work with much larger equipment. Like anything though you get what you pay for when it comes to inverters. 20Watt load is nothing so really any inexpensive inverter will due and can easily be replaced. Just be sure teh inverter has Low Battery Cut Out to protect your battery.
Charge controller is kinda the same thing as the inverter, you get what you pay for, but a 30ish amp CC will be quite inexpensive. I highly recommend PWM and MMPT if its in the budget. Midnite solar makes great small charge controllers in the $600 range, but they also have a 30A guy. I have never used it but always been curious about it. Like I said, I have no experience with this model, but I have many years of experience with their bigger stuff which is industry standard ON AMAZON
Otherwise maybe renogy or victron for real cheap ones? Never used these but I see them all the time on here. Blue Sky and Morningstar make 30A ones, but they may be the same cost as the Midnite. Honestly, if it was me on a small system I would try that Midnite brat or just use a Xantrex/Trace C40. These things are very old now, but they have been used in the indutry for a long time work very well. I service ones that have been running without issue for 20+ years. They used to be the industry standard before more advanced options with displays came along. They can often be found cheap