malofix,
Can you post a picture of your lathe with somehing that shows the size? A view of just the headstock, a section of bed, and the saddle and toolpost assembly could help us help you.
In questions about acquiring tools and supplies, it is sometimes also useful if you edit your profile so that we can see where in the world you are located. (Something like "USA" or "UK" is probably useful enough if you want to protect your privacy.)
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I would agree that a drill press (pillar drill) is useful to have, and some of the small ones availabe at low cost can be OK if you are doing small projects. However, using a drill press to mill has a couple of major caveats:
1. The chuck on a drill press is usually only mounted on a taper and can come loose with the side forces of milling. A mill has the chuck secured with a drawbar so it can't come adrift. I tried the cross-slide vice with end mill in the drill press in the distant past and have a scar on my hand from doing so. In addition, the chuck that comes with a drill is often pretty "wobbly" and the press's bearngs may be not up to fighting side forces very well either.
2. A cross-slide vice is sometimes useful and some of them used to be relatively inexpensive, but they may not be up to the precision of true milling. I have one, and I have used it for special projects, but it's mostly just useful for locating points for drilling holes. ( I can add that cleaning up and adjusting that vice made a good project early in my machining life: Made gibs, deburred ways and edges, replaced shaft bearings with brass and bronze sleeves, and relieved edges of ways and mounting ears for more squareness.)
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My first (and so far still present) lathe was one of the 7x mini-lathes and I ordered the millig attachment along with it. I did use the milling attachment for a while with success. In my case, the milling attachment mounted to the cross-slide instead of the compound slide, which had to be removed. It used the same bolt holes as the compound swivel assembly. Use of a different milling attachment could have been done with an angle plate. The end mills were accomodated by removing the lathe chuck and putting the end mills in collets in the spindle taper (3MT.) You can see that changing from lathe to mill functions is somewhat involved. The capacity of the milling attachment on that lathe is very small compared to the smaller milling machines.
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BTW, I started my machining with a floor drill press, bought the lathe, then got one of the 4x6 bandsaws, then got the mill. Getting pieces to rough size is a time bottleneck best mechanized.
Pardon the long post, but we're glad to see someone else jsut starting their shop adventures.
Good Luck,
--ShopShoe