Yep, stuff costs and it will continue to cost. I think I've exposed about $1000 of film this year alone and that's without mentioning the chemistry or capital equipment. Film photography is not cheap except compared to racing motorbikes

The filters come in a couple of sizes, so at least you know which ones (3") you need. The ones I have are too small for your enlarger. Yes, they do fade with age and lots of use. Make sure you can inspect them before you buy and make sure they all look nice and uniformly coloured (uniform within one filter; each filter will be a different colour). If you find a colour enlarger, the dichroic filters in those do not fade.

You certainly can use the enlarger without filters, the contrast will probably be somewhere around grade 2 on VC paper depending on the particulars of the lightbulb in it. You can also print at higher grades (higher contrast) using graded papers (grades 1, 2, 3 and 4 are usually available), but that's a fair bit more work than just using a single VC paper. The quality is arguably better too with graded paper.

If you're feeling really hardcore, pale blue or magenta gel filters (say if you had one handy) can be used to increase contrast. How much though is guesswork.

You don't need a test-strip machine or contact printer. Cut your paper into 1" strips and expose those under the enlarger one at a time to make tests. Contact printers are handy for previewing a whole roll, but certainly not necessary. You can make contact prints by using crystal-clear (polyethylene) sleeves for your film and sandwiching an 8x10" sheet of paper under the sleeved film, under a sheet of glass under the enlarger. You do really want to find an easel though if you don't have one. A simple 2-blade 8x10" easel should be about $10 secondhand and it's what I use for 90% of my prints.

You might want to try googling for a manual for your timer. And don't bother with APO lenses on 35mm B&W, there is absolutely no point to it because the basic lenses can resolve down to the grain of all but the most crazy-fine (CMS-II) films. The lens you have will work fine if you can clean it - there's probably a locking ring that needs to be undone (metal thing with a tiny notch on two opposite sides), but the lens-spanner to undo them is also going to cost you too... You should be able to make grain-sharp enlargements to at least 11x14" with your cheap lens, so definitely have a good go at cleaning it.