You might find train travel can be disrupted by engineering work on Sundays. Anyway, I have just done a search on www.nationalrail.co.uk for EUS (London Euston) to LLJ (Llandudno Junction) & found the 8.15 departure takes 3 hours 38 minutes to do the trip at a cost of £39 one way. (Llandudno Junction is the nearest place that the Virgin express trains from London stop in order to reach Conway/Conwy in Welsh, which is about 1 mile further on. I would advise that you do a similar search about 10 weeks before your date of travel. This will show you the timings of the trains and whether they will be affected by engineering work. Note that the Advance tickets apply to specific trains & that the fares tend to rise as date approaches - so you should pre-book with www.virgintrains.co.uk as they are the company you will be using. (I would also suggest that you check for the Saturday if you are able to leave London on that day).
www.arrivatrainswales.co.uk operate the stopping trains that call at Conway, so, you may well find that you could get off the express at Llandudno Junction & wait a bit for the stopping train to come. (Put in for EUS to CNY and it will show you how long that wait will be). Alternatively, take a bus or taxi to Conway from LLJ. Don't forget, that you could also stay on the express from London & continue to Bangor - which is the nearest rail station to Caernarvon.
http://www.traveline.info is the site that will tell you the times of the buses from Bangor to Caernarvon. I have just checked for today (Wednesday) and they are every 15 minutes or so and take about 30 minutes to do the trip. You will need to check what they are on a Sunday if you intend to go from London to Caernarvon (via Bangor) on that day. (Just shows that Google don't know everything)!
To get back to Manchester Airport, go to the www.nationalrail.co.uk and put in a starting point in north Wales such as Bangor or LLJ to MIA & it will tell you the schedules. (You may like to visit the English border city of Chester. http://www.visitchester.com.
As well as Conway & Caernarvon, you might also like to visit this place near Porthmadog:> http://www.portmeirion-village.com
Also consider a ride on at least one of these steam trains in NW Wales:>http://www.festrail.co.uk
If going up Snowdon, beware of the weather as things can be going downhill in late October. (Don't pre-book the mountain railway unless you are sure of good weather. http://www.snowdonrailway.co.uk)