Probably everyone got the chance of a good deal flying into Sofia airport but didn't realise that it is quite so far to Sunny beach? I would not reccomend if you have young kids. The journey including flights is really too long. There is no scenery to view as most of the land is flat.
Internal flight to Bourgas:
The best way of course would be to book a cheap internal flights into Bourgas airport and then get a taxi to Sunny beach, which is about 35 mins away. Here is the link for flight details: http://www.air.bg/en Free tea and coffee on Bulgaria Air flights too. You can consider flying to Varna airport then going to Sunny beach by taxi. Journey takes 1 h 30 minutes.
You can get a bus from The central bus station to Sunny beach for a reasonable cost. There are a few companies that do this. Some buses are direct from Sofia to Sunny beach, 14.00 PM takes about 6.5 hours. Depending upon which bus company you take, it stops once or more times to pick up / drop off. Ticket price 32 lev. Look on the Sofia bus station web site for alternstive times. The bus and train station are next to each other. You can get the metro from terminal 2 or book our taxi at fixed price. http://www.bgrazpisanie.com/en
There is the train but very slow about 7 hours or you could book the sleeper train from Sofia the train is ok and clean. If you get a Train to Bourgas you have still to get to Sunny Beach. Try the Bulgarian Railway Website: http://www.bdz.bg/en/ If you do decide to do the train always ask for 1st class. There is new metro line connecting Cenral bus / train station with T2 on the airport. The metro line operates between 5:30 – 24:00 h. Night sleeper can be booked on-line 20 days in advance (30 days in the summer) Better book soon as the cabins were released. There are 30 cabins on the train, only 5 can be booked on line.
The other options is to book a private door to door taxi transfer to Sunny beach. The taxi journey takes 4 h 30 min as Sofia is 413 km. away. Consider private transfer if there are more of you. Have a look for prices: https://bg-taxi.com/transfer/sofia-airport
Driving across Bulgaria would be a great idea. Hiring a car gives us the flexibility to stay a couple of days in Sofia or Plovdiv, one of the oldest towns in Europe. Old town is definitely worth seeing. Note fuel is not that much cheaper than the UK. Generally the roads are quite good. Get a quote here: https://bg-taxi.com/carhire
Parking near the airport:
There are several car parking options available near the Sofia airport and one of them is at hotel Ibis, 7 bg leva a day, secure car park, underground section too. It includes a free transport to the airport. Another hotel with cheap and secure parking is ATM. Also comfortable rooms and good food. Bus into Sofia as well. They do a free airport shuttle. If you stay at Best Western hotel and then parking is free. They run a free airport shuttle both ways too. http://parkandfly.bg near the Ibis is 40 leva a week under cover secure car park and transfers included. Another cheap parking is LC car parking near the traffic lights by Terminal 1.