Hello there,
Yes you can do polytechnic after your 10th. It is a good decision. After completing your polytechnic, it is better if you get admission in an engineering college. The chances of getting job is higher in this case. You can get admission directly in the second year, after you complete your polytechnic course. The most popular option for polytechnic diploma holders is to take up B.Tech course.
Hope this answer helps you.
Good luck!!