What weld process you use is not as important as the geometry of what you intend to make with the welding. Each of the welding processes, while having slight variations, works in basically the same way by generating some heat and melting the metal and then letting it re-cool. Whether you use some form of arc welding or torch welding (or electron beam welding for that matter), matters a lot less than how you treat your weld and how strong the surrounding structure is.
What may determine what you use may be the material of the frame. If its a steel frame then an oxy torch will be fine, if its aluminium, you'll first find it almost impossible to weld and you should use a MIG or TIG welder to keep the weld pool covered in inert gases.
Keep in mind that the welded patch of metal will be more brittle than the surrounding area because it will harden due to the local heat treatment, try and smooth off the area around the weld afterwards using a grinding wheel or similar to make sure you don't get crack propagating through the weld from any sharp changes in geometry.
That's quite a long answer but I would guess an oxy torch would be fine if you know how to use it.