I've been looking into DIY'ing mini-splits, which also entails looking into some basic AC items.
Things for you to consider. . .
1) Ducts are sized differently for heat than they are for heat and A/C (well AC really):your ducts might not be ideal.
2) Oversizing can result in short cycling, less than ideal reductions in humidity, and I think frozen coils. At the very least you need a assessment of how many cooling btu/tons you need; I suggest a manual J calculation.
3) Many companies do not honor their warranty if the system is purchased online or DIY'ed on the install (at least in mini-splits); you will have to find a warrantied one or accept the risks.
4) You will still need to run electrical to the outside unit.
5) You will have to punch holes in your house; that is always stressful to me no matter how many times I do it.
6) You will need special tools to do the install properly; a vacuum pump to evacuate the lines, a pressure gauge to determine the correct level of vacuum, nitrogen tank and regulator to flush the lines and pressure test, and possibly a flaring tool to fit the lines. At a minimum.
7) Refrigerant: there is A LOT of arguing on the internet, but from what I can tell if a unit comes pre-charged with R410A you can DIY release the change, but the pre-charged ones have a set distance of line if you need a longer run then more refrigerant is needed; at that point I believe certification is required.
8) I have read many a story about HVAC service companies refusing to work on a DIY install.