Hey,
You can look for hostels or zostels for cheap stay ( www.hostelworld.com ). You can also book hotels at Oyo, MMT or Trivago at minimum prices.
Try to book your hotel 4-5 km far from main area to get at low rates( North Goa-Calanguate beach is main area) if you are planing to wander Goa by hiring bike or scooty.
Hope this would help you.
Hey bro,
Arambol has lots of stay options ... hostels are few ...
Mentioned few :-
1. Namyo hostel -
Khalchawada, Arambol Beach Arambol, Pernem, 403524
07020348432
2. Happy Panda hostel -
Mandrem road, Arambol, Goa 403524
http://happypanda.in
09673201979
3. Wanderers hostel -
Madhla Vaddo, Opp. Nanu Wines, Morjim Beach Road, Morjim, Goa 403512
http://www.wanderershostel.com
09619235302
Old goa too have affordable options :
Here are few with the link to book rooms :-
1. Old goa residency -
Near Old Goa Fire Brigade, Goa 403402
https://www.goa-tourism.com/old_goa_resi
08322285327
2. Ginger hotel goa -
Plot No. 37 & 38, SGO Complex, Near Passport Office, EDC, Patto, Panaji, Goa 403001
https://www.gingerhotels.com/ginger-goa?utm_source=Google_Business_Listing&utm_medium=google&utm_campaign=GINGER_GOA_BUSINESS_LISTING
0832664333
3. Hotel Palacio de Goa -
Doctor Gama Pinto Road, Behind Pharmacy College, Panaji, Goa 403001
http://www.palaciodegoa.com/mobile/
08322424289
other cheap stays are :-
Hostel Zostel in Calangute
Backpacker panda in Candolim
Little India beach cottages in Baga
Sai Palolem beach cottages
Nikita Residency in Calangute
Anjuna palms guest house near Anjuna beach
Morjim sunset guest house is also good to stay in goa for reasonable rates ...
Happy Travelling Bro!!!