ER16 will hold up to 3/8 tooling.
One word of advise, don't let your budget determine your requirements, determine your requirements and then work it into your budget.
I've cut tool steel without any issues using a 10mm 4-flute end mill at depths of 0.200in (5.08mm) and the motor you power it with is just as important as the spindle is, a small motor may not have the power required to keep the tool turning when cutting hard material and more power means more money and explains why real spindle motors cost over $3000.00 (I'm working on a reasonably priced solution).
Working strictly based on a small budget and you will make many sacrifices in your machine design so plan well, decide what your minimum acceptable requirements will be and do not go below them.
Making a larger VMC and using BT15/ISO15 may not be in your best interests unless you're making jewelry so I suggest you plan your machine size accordingly.
A work area of 16.5in x 9.25in or 24in x 6in are a suitable size for BT15/ISO15 or BT20/ISO20 and the 16.5in x 9.25in tables are available for about $300,00 with 1/2in T-Slots and are suitable for 20mm linear rails which aren't too expensive.
If you want to use 1/2in tooling then I suggest BT20/ISO20 (at a minimum) or BT30/ISO30 (recommended) but these will cost you more and you should budget accordingly.
You can make a fairly rigid small VMC frame using 4in x 8in x 35in (1/2in wall thickness) rectangular tubing and 12in x 4in (1/2in thick) channel for the base and 1in x 2in cold rolled for rail seats for about $300.00 in material and about another $175.00 for the material to make the XY carriage leaving you only the Z head and table to figure out and will weigh in around 500-800 lbs when the frame is assembled (not fully assembled machine weight), my Z head assembly's average weight is around 250lbs with spindle motor attached for a machine of this size and since I add a 6in x 1/2in thick skirt to the channel base and weld in some webbing for added rigidity my frame weight before servos is around 1000 lbs.
Going to an 8in x 8in x 35in (1/2in wall) square tubing will increase rigidity well beyond the needs and you can get away with a 3in x 7in x 35in (1/2in wall) rectangular tubing and still have good rigidity if you design it well.
Those round column mills you see have a 5in or 6in round column with 3/8 wall thickness (depending on the make/model) and they're fairly rigid but the head will shift on the column if it is not keyed and most aren't.
I personally dislike round columns and dovetail on small machines, dovetail machines are the greatest waste of table size vs table travel - 30in long table has 20in of Y travel, linear rail carriage designs allow for greater than 100% table travel and the carriage is roughly about 1.5 times the length of the table so the footprint is smaller for the same size of table travels so plan your machine well.
If your thinking about aluminum extrusion or 8020 material as a frame then rigidity isn't a priority and precision is pretty much non-existent as well as machining hard materials.
Another thing I recommend, since your going to buy ballscrews for your machine build, buy DFU1605 or DFU2005 and not SFU1605 or SFU2005, the double length nut will handle the required loads of a milling machine and last significantly longer.
If you can't afford $1200.00 for a real CNC panel then a breakout board and Mach3 or EMC2 is something you can consider but realize, software based solution are not really cheap if your looking to get any real precision out of it, especially using stepper motors, this brings you back to your budget, plan accordingly.
I use only servo motors in a VMC, you can get a set of 60mm 4/5 HP servos and drivers for around $1500.00 shipped or a set of 90mm 1.5HP servos and drivers for $1900.00 shipped.
1600Oz Nema 34 Stepper motors cost around $130.00 shipped form china, add a suitable driver and power supply for another $150.00 looks great on paper but, 1600Oz only occurs below 50RPM and despite what they claim, power drops as RPM increases so you wont have sufficient power at 1000RPM and you'll never see 2000RPM out of a stepper before it stalls trying to move your axis so your $800.00 stepper kit while looks like a saving, has actually cost you performance and precision.
This is why it is common to see a 4:1 (or higher ratio) belt pulley setup with stepper motors to increase available power and sacrifice rapids to 80in per min and maximum feedrate to 25in per min.
Lastly, if your budget is really small (less than $1500.00, forego making a machine and buy one that is within your budget, you may not get what you want but you will get something, in most instances these machines are not suitable for CNC conversion since the mass/rigity is not there and the hardware (like lead screws) is just not suitable and the cost of conversion adds up quickly.
If you've never owned a CNC mill, I suggest you might want to start off with a sherline or similar so you can get a feel for it before you dump a wheel-barrow full of pennies on a machine or build, I've seen it many times, people ask me to build them a frame and I do, then it sits for years unfinished because they didn't realize that this is an expensive hobby to be in or that to get what they want isn't as cheap as they thought it would be.
I am trying to provide affordable solutions for things like spindles but there is no way to make the $350.00 ATC spindle that everybody wants unless I can do quantities of 10,000 and I don't have the funds to do this or 10,000 people beating my door in to get one and pay in advance.
Even if you managed to make a shaft for your own spindle conversion, heat treating will run about $160.00 for the one shaft because you need to temper and harden and then grinding will cost you at least $250.00 due to setup and time if you don't know someone with a bore grinder who will do you a favor on the cheap and these are just some of the hidden costs that are never explained.
Making things in quantity helps lower costs, I can heat treat 10 shaft lots for $400.00 a lot so this breaks down to $40.00 a shaft and $40.00 sounds great but I have to do 10 shafts which means I need to sell at least 10 spindles to be able to get this price so I can sell at the low price I do.
AC bearings are another expensive thing in spindles, high quality precision AC spindle bearings cost $350.00 a pair (matched set) if I buy 200 pairs direct from the manufacturer, if I buy 1-3 pairs then the cost is about $250.00 each, luckily we use this size for some HAAS and other manufacturers shafts so I can bump up the quantity 50 pairs and pay a little less than $300.00 a pair.
Everybody wants a low price and they want to wait for the low price before they buy and the reality of it is this, if they want a low price then they have to buy now, by increasing production volume I can lower the price, if waiting for that lower price is your game then you'll never get one at the price you want and it has been decided that only those who buy on kickstarter will get the lowest price, if funding is exceeded then they will receive a partial refund based on the production cost savings, those who purchase later will pay more than the kickstarter advertised price as one of the guys in our group will be matching the kickstarter funding so he can have stock on hand for those who wish to purchase later and he will expect a profit on his investment and rightly so deserved.