All the real Arduino boards and clones thereof have at least one UART, and an ADC (typically 6, 8, or more channels).
Note that those are TTL serial (5v, 0v voltage levels) - while real RS232 is -15v ~ +15v - so if what you're interfacing with really is RS232, you will need the TTL serial to RS232 converter (eg, max232 or equiv) - though a significant portion of "RS232" devices are actually TTL serial, and are using the name inaccurately.
The Uno is recommended for people who are new to Arduino (Nano has same processor, but in much smaller, cheaper form factor)
HOWEVER - One can make the case for using a board with more than 1 serial port, since you may want to use the serial monitor for debugging or other purposes while communicating with that other serial device. You could use software serial (but this comes with caveats) for the other device, but that can only send or receive at any given time.
If you need serial monitor plus a robust serial port, you could use:
A Leonardo (or Micro) - these have native USB support, and a UART, and the USB port by default is used as a USB-serial converter, leaving the hardware UART free for whatever. (capabilities other than that similar to Uno/nano/other 328p-based boards)
A Mega2560, which may be overkill (256k flash, 8k ram, tons of pins), but has 4 hardware UARTs
A 1284p-based board , with two hardware UARTs (and 128k flash 16k ram, and a few more pins than an Uno/etc), one of which would be used for programming and serial monitor, and the other for that device. There aren't any official ones, but the unofficial ones are reasonably well supported. (Crossroads on the forum sells a few versions).
Considering that you're new, I think that a Leo/Micro would be the best choice for you, since it gives you an uncontested hardware UART, but is an official board, and you probably don't need the functionality of the Mega2560.
It looks like DrAzzy has covered your options pretty well.
I just thought I'd point out there are a lot little PCBs available with include a connector and a MAX232 type chip. Using one of these boards may be easier than using the chip by itself.
Here's one example of these boards. The MAX3232 chip mentioned is very similar to the MAX232. I think the main difference is the MAX3232 has a wider range of possible supply voltages (to make it easier to use with 3.3V devices).
I haven't used the board I linked to. I've always used the chips with the needed extra parts but if I had know about these inexpensive boards back when I needed to use RS232 I would have probably used one since the boards cost less than what I paid from the parts.
As DrAzzy mentioned, the term "RS232" is often used incorrectly. Based a quick Google search, I'd say you're probably correct to think you need to use RS232.
What voltage is this analog? Does it go below zero volts like an audio signal?
What accuracy? Most Arduino chips are 10-bit, which means they can represent a range of values from 0 to 1023. Some have 12-bits but for higher accuracy like 16-bit, you need a dedicated converter, which will often talk to the Arduino over I2C or SPI.
How often are you expecting to sample this analog signal? Have you worked out what baud rate that is for your desired sample frequency and bits, not forgetting to add the RS232 start and stop bits plus whatever packets or delimiter characters your downstream device requires?