I’m not sure where you are based, but non-stop economy class fares to Istanbul are available from Delhi for around Rs 50,000 (there are longer, one-stop hauls from about Rs 40,000—you can opt for them if you can make more time). The visa will take away Rs 4,700, which leaves you with about Rs 50,000–70,000 (outer limit) to spend. As a single traveller, this looks quite achievable, although you may not be able to afford B&Bs everywhere. Pick a mix of hostels (www.hostelworld.com/hostels/turkey); rental apartments, so that you can cook a bit to save money (www.apartsturkey.com, www.airbnb.com, www.homeaway.com, www.flipkey.com); and B&Bs (www.hostelworld.com/bed-and-breakfasts/turkey, www.bnbfinder.com/turkey-bed-andbreakfast), to stay fastidiously within your budget. As for exploring Istanbul via public transport with a guide book in hand (or, sometimes, tucked away into your bag), go for it!
Now for what isn’t going to be that easy: eight days, you must know, can never been enough to see a country, especially when you enjoy detailed self-exploration, and then Turkey’s fabulous sites are scattered about. Izmir, Kusadasi and Pamukkale lie clustered to the south of Istanbul; Cappadocia is away eastward in central Anatolia. You’ll have to enter and exit from Istanbul anyway for the cheapest airfares. It’ll be tiring to proceed right away on the rest of your itinerary, and then it depends on how the connections work out, but you can head for Izmir and bus it over to Kusadasi (I must say I find it curious that you prefer them over Ephesus, going by the rest of your choices). There are plenty of day tours to Pamukkale from Kusadasi. Then fly Izmir-Kayseri for Cappadocia (connections are not available on all days, so you’ll have to adjust your itinerary sensibly to fit them) or take a train to Ankara and then a bus to Goreme (5 hrs) or Nevsehir (4.5 hrs).
I would advise you to prefer trains (yes, trains, not Turkey’s famous buses), which are a reliable, comfortable and inexpensive way to see more of the country, especially because convenient overnighters will save you the cost of a night’s accommodation, but connections can get tricky. For example, the station at Pendik is 25km east of central Istanbul, accessed by ferry, metro and taxi over two hours of travel (all details at www.seat61.com).
Worry not if this isn’t your thing. Airfares are equally if not more affordable, so pick a cheap fare from an aggregator like www.aerobilet.net or try any of these low-cost airlines: www.anadolujet.com/aj-en, www.atlasglb.com/en, www.borajet.com.tr/en, www.onurair.com/en, www.flypgs.com/en or www.sunexpress.com/en.
Cappadocia is a region, we tend to forget, and it needs three full days by itself—a long first day at the rock-cut monastery of Zelve Valley, the open-air museum and bazaar of Goreme, and the rock city of Uchisar, with several opportunities to climb for better views; another day for the underground cities of Kaymakli and Derinkuyu plus a hike in the Ihlara region, and the final day for exploring Cappadocia’s valleys, Mustafapasa and Avanos, shopping in Urgup, and may be even catching the 9pm show of whirling dervishes at the Sarihan caravansary. Fly back to Istanbul from Kayseri, or take an overnight sleeper train back from Ankara. You can easily book guided tours well in advance from reliable and responsive operators like www.yukitour.com, www.baltactours.com or www.constantinopleguide.com (on email, of course, and, these days, even on WhatsApp).