Rotterdam is a safe, expat-friendly city and you can find affordable housing within the city itself.
I'm not sure if you are familiar with the Netherlands or not, but in urban areas, you are never far from a grocery store. They favor smaller, local grocery stores over larger suburban centers, although those exist as well. They also tend to favor shopping areas with a number of smaller stores over hypermarkets like Carrefour you see in other European countries or supercenters like Walmart in the US. Rotterdam has several of these shopping areas so you will also never be too far from other stores you might need to visit.
Public transportation in Rotterdam is also quite good. Generally, you can get anywhere you want within the city via bus, tram or metro within 30 minutes. Rotterdam also has a number of smaller train stations that are one or two stops away from the central train station, where you can board the train to Brussels. These are Rotterdam Zuid, Rotterdam Lombardijen, Rotterdam Blaak, Rotterdam Alexander and Rotterdam Noord
Crime levels in Rotterdam, like all of the Netherlands, are pretty low. I lived for a year in Charlois, which is the "least safe" part of the city according to https://wijkprofiel.rotterdam.nl/nl/2018/rotterdam, and never once felt unsafe. There are some individual parts of some neighborhoods to avoid, but you're unlikely to ever end up in those.
If cost is your most important factor, I would suggest where I lived in Charlois, which is in Rotterdam Zuid near Zuidplein. Rotterdam Zuid is the part of Rotterdam south of the Maas river. My wife and I lived in her 2 bedroom, 55 square meter apartment for about 1 year and we managed with our infant daughter for about 3 months of that. You should be able to find larger sized apartments in that area for under 1000 euros a month that would be quite comfortable. This part of Rotterdam is quite cheap and Zuidplein is a good shopping center with a bus station for many regional buses and a metro stop connecting to the center of Rotterdam.
If you prefer a little bit more popular part of the city, the neighborhoods around the center north of the Maas are reasonable choices.
In terms of contracts, you can find short term rentals, but those are typically arranged through housing corporations or companies that specialize in renting out apartments. Typically, leases are for 1 year. There is generally no maximum length, but contracts will typically allow for an annual rent increase based on the cost of living increase. Tenants have strong rights in the Netherlands and once you start renting a house or apartment, you generally have the right to stay there as long as you want.
In my experience, renting housing in the Netherlands takes some legwork. There is no single central resource that can help you find all housing for rent in a given area. You can find some through real-estate search engines from the big realtor associations (NVM: funda.nl and VBO: vbo.nl) but their primary focus is on houses for sale. You can also check individual realtor websites and companies like Rots Vast (rotsvast.nl) that specialize in renting houses and apartments, but each of these will be company specific. I would also strongly suggest asking your new company if they can assist you with finding a place to live as they may have some more local connections that you can take advantage of.
If you don't mind being a bit further away from the action and would like a bit more "traditional" Dutch city, I recommend taking a look at housing in the smaller cities of Gouda or Delft. Both have good train connections to Rotterdam.