Have you actually looked at listings in the area? You will be hard pressed to find a house, or even a townhouse for that price anywhere in Oakville or Burlington. If you want to be close to work, it would most likely be a condo apartment. If you are set on a house, the decision as to where would be made on availability of something suitable. If you are leaning toward a condo apartment, why not Mississauga? If you have to look for work in Toronto in the future, it would give you more commuting options.
Have you done the drive from Hamilton to Oakville during rush hour? The 403 is not a highway I would ever choose to be on at those times. If you can shift your commute times, then Hamilton might be an option. Prices have been rocketing up there also for the past couple of years, so your options still might be limited.