Sobha Elan in Ganapathy has 1 BHK apartments costing Rs 40 lakh, and Sowparnika Beetal in Nanudapuram having 2 BHK apartment in the range of Rs 42 lakh to 45 lakh, would be ideal for you, since they are priced according to your needs.
I don't really know of any locality specific projects, but since i'm from Avinashi Road, i'll tell you about Chathamkulam Anchal project. The project has 2 BHK and 3 BHK apartments priced at Rs 41 lakh and Rs 48, respectively.
I know about Muktha Rajmangala in Edayarpalayam which has 2 BHK apartments with different floor areas available within the price range of Rs 44 lakh to Rs 48 lakh. Another one is Vamanas Athulya in Ganapathy, with 2 BHK apartments costing around Rs 42 lakh.
Vijaydeepas KTVR Grandeur in Velandipalayam has 2 BHK apartments priced at Rs 42 lakh, and Swarnamangal in Vilankurichi Road has 1025 sq ft, 2 BHK apartments at a cost of Rs 45 lakh. Both these projects are good, and should fit your needs.
I know of two projects that meet your budget. The first is Provident Green Park in Selvapuram, which offers 3 BHK apartments at a price of Rs 43 lakh. Nivasan Blue Haven is the second one, with 1200 sq ft with 1200 sq ft, 2 BHK apartment costing Rs 39,9 lakh.
Hey, Saravanampatti has more projects than listed above. Sree Daksha Kshiptha has 900 sq ft, 1 BHK apartments priced at Rs 42 lakh, and Jass Dwarka provides 1200 sq ft, 2 BHK apartmetns at a price of Rs 37 lakh.
There are plenty of projects to choose from in the price range you mentioned. Some projects in the Saravanampatti region are Vardhana Constellation with 3 BHK apartments costing around Rs 40 lakh, and Vivant Eleganz priced at 36 lakh for 2 BHK.
Yes, Ganpathy has a couple of project that fit the bill. Coral Ennar with 2 BHK apartments costing some Rs 40 lakh, and PNR Tripathi having 2 BHK apartments at a price of Rs 37.5 lakh are both pretty decent projects