If you are looking at rowing for fitness, you should look at rowing shells, dories, wherries or other boats designed for oars. You don't use oars and rowing in kayaks, you use a paddle that is not attached to the boat. Quite a different technique.
Nothing in an inflatable kayak that you can get new in that price range would be remotely seaworthy. Cheap inflatables are akin to pool toys -- slow, hard to paddle, don't track straight because your weight makes the middles sag, a lot of drag and susceptible to wind and currents. Far too easy to get swept out past where you would be able to paddle back to shore. Think of it this way, would you try to paddle an air mattress off shore? That's about what you would be doing. When I was living in Michigan about 10 years ago the Coast Guard got so tired of having to retrieve and rescue people who got swept out past their ability to paddle back in on Lake Michigan that they began to hail and turn back people from leaving the sheltered bays in cheap inflatables and open cockpit short rec kayaks, especially on days of strong winds and undertow.
There are $1000 to $4000 inflatables and inflatable/folding hybrids that are seaworthy, from a few of the higher end Advanced Elements and the Pakboat XT models to the top of the line Feathercraft Java. But you need length and rigidity in order to have safe control and ability to produce forward momentum for coastal paddling.
There is someone selling a used Pakboat Puffin inflatable/folding hybrid kayak in the P.net classified ads right now for $475. I have one of these and it is a decent little boat. The metal frame makes it more suitable for serious water and with a spray skirt and flotation bags under the deck bow and stern it would be marginally suitable for mild coastal conditions for an average sized person. But it would not be my first choice for that because it is a bit wide (28" ) and a bit short (12').
At any rate, you should not attempt to take any kayak out into the ocean or river deltas that feed into it until you have had some qualified instruction in paddling and safety techniques and orientation about tides and the dangers that they can create for paddling.
If your main constraint is budget, there are free instructions to build your own inflatable or folding kayak at http://www.yostwerks.com
It can usually be done for under $300 in materials.
You can also find used seaworthy plastic kayaks for under $500 if you are willing to look for them and educate yourself about what models are suitable.
But it sounds like you don't have much experience with kayaking. I agree with the other answers that you should try it out a few times with an outfitter or sign up for a class in kayaking to get properly oriented so you have a better understanding of what you want to do, where you want to do it and what boat and equipment would suit those purposes.
PFD's (Life Jackets)
Free Standing Boat Racks
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