Gasless only welders have not been listed as they cannot be recommended and I have no wish to use them. However all gas welders can obviously weld gasless via changing the wire to one with flux.
The Wolf MIG 140 Welder
is the cheapest usable welder found on the market with build quality and functionality that you would expect for the price range, definitely not a profession welder. Common issues include gas line leak at handle, torch going permanently live due to a short circuit on the micro switch and wire feed failures.
Ideal for a first welder to test your interest; however limitations and reliability will force you to upgrade for frequent usage. I would recommend starting on max power and gas flow settings and working back on first use. The version shown below includes the shielding gas attachments. The attachment is for the disposable gas bottle included, an adapter will be required to attach larger non-disposable bottles if required.