FHA is the way to go if you're short on cash; you can put at little as 3% down, though you will need to pay monthly insurance and a significant upfront fee (basically pre-paying the interest). If you qualify for a conventional loan, you can ask for seller assist (up to 6%, if you put 10% down, so it's possible to get close to FHA terms and avoid some fees and the extra inspection, if your credit is good enough). Talk to a mortgage broker about what is possible here.
Generally a gift can't be borrowed; the lender will "source" the funds to see where they came from. The down payment definitely has to be real savings from past income. *Maybe* a gift from a loan is possible if the borrower is not the buyer and the agreement is not contingent on it; it's really up to the lender what they're willing to accept.
My main concern with you would be making sure you're really ready to buy. Home ownership comes with lots of new expenses; you're now fully responsible for *all* utilities, maintenance, repairs, etc. (Do you have a lawnmower?) You will probably need furniture, moving expenses, and so on.
Because of these expenses, you don't want to use *all* your savings on the house. You don't want to be completely broke after closing! Nor do you want to be right at your debt limit immediately. There will likely be some minor inspection issues you'd want to fix right away; if you neglect them, they can turn into bigger problems later.
Are you considering taxes, mortgage and homeowner's insurance in the mortgage payment? Hopefully it will still be less than your rent! You'll want to continue saving after the purchase, at least 1% a year, so that you have some reserves in case you need emergency repairs, maintenance, or other unexpected expenses. Careful budgeting and controlling expenses will be very important as you go through and adjust to this major life change.
Be sure you have adequate income and reserves to survive moderate adversity. This is how foreclosures happen: you exhaust all your savings and are at your debt limit after the purchase -- then the car breaks down, sombody gets laid off or sick, you miss a couple payments, and suddenly you're fighting to keep your new house.
Once you have some equity in the home, you can get a line of credit against the house as a form of insurance against sudden large expenses (better than putting it on a 20% credit card -- another way bankruptcies and foreclosures happen), but nothing beats good old-fashioned cash reserves.