I use a higher-up package but try hostarmada as their support is outstanding, and the prices match their service. Just my 2 cents, make sure you read the service terms, as they raise the price after the first year. I hope this helps.
How is your experience with NameCheap, their cheapest plan is $4.48 which is within budget
Namecheap is good, best for low-budget projects. their support is also great.
my experience with namecheap is also quite good. customer service always help and stuff works on the shared hosting. But like others said only for small projets