I disagree with the statement that the agent is only out to make the sale. While it is obviously to their advantage to make the sale, a good agent will never pressure you. We've only bought two houses in our life, but in neither case did I ever feel the agents were in it for their own advantage as opposed to mine. On the contrary, they did quite a lot of work to find a house for us based on what we wanted.
My advise will be to actually go to a reputable agency and talk to an agent directly. Tell them what you want/need. They will pull a list of properties that more or less match your criteria, and can often show you 3 or 4 properties in a day. That way you will also get a feel for the market. A good agent will also indicate to you how flexible a seller is with their asking price.
As for offering more than the asking price, be careful with that, once you put in an offer and it has been accepted, you are protected by that contract. The only way for you to be "upstaged" typically, is if the seller gets a higher _CASH_ offer.
Also be very careful of putting up all your savings for a deposit. Use a transfer cost calculator (something like
https://www.rawson.co.za/transfer-cost-calculator) to get an idea of extra costs needed. Don't worry about who's calculator it is, the amounts are determined by SA property law. Things like transfer duty and attorney's fees need to be paid separately and can not be included in your bond usually. These amounts typically need to be paid long before bond registration anyway (which is when the bond money is paid to the seller). Typically on a R1,000,000.00 sale, this will be in the area of R55k (depending on your deposit & actual bond amount). This is the minimum of how much you need over and above your deposit.
Another thing to remember is that any fee you pay before hand (such as your deposit) is paid to the transfer attorney, who will keep it in a trust account. You will not be able to have access to that money before the sale is concluded. Also remember that any money paid in advance usually go through the transfer attorney. If anyone else (like an estate agent) asks for money to be paid elsewhere, first contact said transfer attorney to verify this. The trust account interest should be paid back to on the conclusion of the sale, but this is typically not a very large amount.
ALWAYS VERIFY ACCOUNT NUMBERS THAT YOU PAY MONEY INTO. Phone the recipient (after verifying said recipient through the transfer attorney) on a number found using a medium other than the requesting email to verify the account number in a separate channel. I'm not trying to be a scaremongerer, but on more than one occasion has a deposit been lost due to an email scam. And no-one will refund you this money.