Sorry to wave my 50 years in a machine shop around like it was an actual badge of authority but be guided by my experience. I worked in a production and repair shop or many years and in all that time I used flood coolant maybe 5% of the time in the heavy tool section where I spent most of my career. When I worked in the lathes and mills I used it about 20% of the time and in vertical turret lathes maybe 40%. It's great stuff used when needed and in a high volume production setting a good coolant selected for the work and the operations will add 15% to the day's production and reduce the tooling costs about the same.
Look into your actual requirements. Ask yourself these questions: How often do you actually need coolant to improve tool life, carry away cutting heat, improve finishes? Do you make over - say - 20 lb of chips pr week? Are your running a small commercial shop, a nights and weekend home shop, or a hobby shop? How do you intend to use coolant? Flood? Squirt bottles. Spray mist? Brush on? For what material? Steel? Tough stainless? Aluminum? Refractory metals? What operation? Production machining? Threading and form cutting? Why oil only when occasional use of water based coolants is so efficatious, particularly for deep drillings and distortion control? How do you intend to deal with tramp oil and tramp water?
In my home shop, my rule is never run flood coolant unless it's actually called fror. In 44 years at my present location, I've never filled my coolant systems even in weeks where I generated hundreds of pounds of smoking hot chips making 4" oyster dredge sheave pins from 6" line shafting. I squirt, spray, dab but never flow it on. When streams of coolant meet rotating parts and tools you get splash. Coolant flies everwhere including out on the floor un-noticed unless you have a good coolant containment system. Flood coolant in the home shop is plain too much mess. I have a good 17" lathe and a basic 9 x 42 turret mill. I've never run flood coolant on either. Most of the time I cut dry but with my arsenal of bottles and cals handy for when I need them.
I have a laundry squirt bottle of mineral lard cutting oil and a bottle of soluable oil. I also have a few cans and bottles of stuff like Magic Tap, Rigid Pipe Threading Oil, WD40 for aluminu (wonderful stuff as an aluminum cutting agent), Chesterdon areosol cutting fluid, and stuff like hand cleaner, bacon grease, and a few witch's brews of my own devising for when I have visitors and I want to seem mysterious.
So, do you have a well designed splash containment? Do you work with difficult materials or work your machines full time? Make chips by the bucketfull? No? Start a bottle and can collection.
All that said if you HAVE to run oil based coolant run a simple mineral lard cutting oil. It's a good general ourpose coolant that keeps well in sumps for years. There is little difference in most mineral lars oils sold as coolants. Any differences claimed is mostly hype. Buy a name brand if you wish but house brands work well too. If you have to cheap out and have access to low cost petroleum products for cutting oil use a light hydraulic oil NOT red dyed ATM. The red dye gets everywhere and will permanently stain paints, work clothes, and concrete floors. Useing chainsaw bar oil on machine tools - well, I won't go there.
Strong emphatic message: Do NOT use motor oil on a machine tool because it's designed to be hygroscopic. Motor oil if used on your machine may cause film rust in cool weather and may stain or varnish if left fror wreeks. Motor oil is designed for internal combustion engine where it works super well. A machine tool has none of the operating characteristics of an internal combustion engine. Use the lubricants reccommended on your machine's lube chart cross-indexed to equivalent lubricants available locally.